In Interesting Times, Rincewind invokes this trope by informing enemy soldiers that there were definitely no invisible blood-sucking ghosts, said ghosts had not been grown to twice their size by the Great Wizzard [sic], there certainly weren't 2,300,009 of them... He was quite proud of the "9".
In the same book, Vetinari certainly did not receive a missive, which was not delivered by Albatross from the mysterious Counterweight Continent: Indeed, he has no contact with that far-away mythical place whatsoever. The missive, which as we all know does not exist, does not contain a message requesting the help of a "Great Wizzard".
A certain copper in Night Watch: "And for close-up fighting, as your senior sergeant I explicitly forbid you to investigate the range of coshes, blackjacks, and brass knuckles sold by Mrs. Goodbody at No. 8 Easy Street at a range of prices to suit all pockets, and should any of you approach me privately I absolutely will not demonstrate a variety of specialist blows suitable for these useful yet tricky instruments."
That selfsame copper in Thud! cynically muses on whether "community leaders" are really the ones saying "do not use the shiny new axes in the cupboard... no, not that cupboard, this one right here."
Terry himself gives a suspiciously specific denial in Thud. Two troll thugs working for the troll crime boss Chrysophrase tell Commander Vimes that their boss wants to see him, and one of them makes the mistake of threatening Vimes and his family; later, when the two meet, Chrysophrase casually asks Vimes if he wants some gravel for his garden, and shows him a box that couldn't possibly hold an entire troll.
The Watch books have a recurring minor character called "Done-it Duncan", who will confess to anything if prompted (including stealing fire from the gods - of course, he was a bit younger back then). This actually makes him a useful informant, as most of his confessions are along the lines of "It wasn't X who did that, it was me."
Discworld features a couple of Suspiciously Specific Assurances too: Nobby Nobbs is definitely human. He has a little paper to prove it. Jeremy Clockson has one, too, to certify his sanity to anyone who asks. (In Nobby's case it's probably true, but the very fact that he carries the paper around makes people even more suspicious. And in Nobby's case, his documentation only states that he's probably human.)
In A Hat Full of Sky, Daft Wullie attempts to corroborate his brother Rob's tale of being thrown out of Fairyland for rebelling against the Queen by adding, "Aye, and it wasna because we wuz totally pished at three in the afternoon, whatever any scunner might say!"
Sergeant Jackrum, one of the Discworld's great liars, makes full use of this trope in Monstrous Regiment.
Sergeant Jackrum is telling the truth, though. Sergeant Jackrum is not a violent man, because she's a woman.
Averted by several trolls, who are specifically noted as having found that the general denial "I never done nothing" works better than specific refutation.
In Witches Abroad the witches are begging from house to house, and 'not coming directly here by any manner o’ means'.
Terry Pratchett himself has denied that FourEcks is based on Australia, although he admits it might appear a bit small-a-australian.
He also frequently references it when referring to statements put out by the (U.S.) Government. If the government says "not X," then "obviously" X is the truth.
Subverted in the Hercule Poirot novel Dumb Witness. Because a suspect denies putting strychnine in the victim's soup, the detective knows that the man is specifically avoiding mention of arsenic. Despite this, the man is innocent and the victim was not killed using arsenic, the man is just trying to protect his sister, who he thought had killed their aunt with arsenic.
Invoked in one of The Destroyer novels where Remo sneaks past an annoying security guard by vandalizing a public bathroom and loudly insisting to a bunch of reporters that "The guard had nothing to do with it."
In the YA novel Sprout we have the main character, Daniel, AKA Sprout, who becomes close friends with new student, Ty, in a Kansas high school. One afternoon they hang out in Ty's back yard where Ty shows Daniel the lake his twin brother drowned in when they were eight. Ty is about to cry and as a comforting gesture, Daniel places his hand on Ty's shoulder, at which point Ty shouts at him: "Dammit, Daniel. I'm not gay!" and proceeds to run into his house.
In the Doctor WhoPast Doctor Adventures novel Grave Matter, the Doctor is trapped in a Big Scary House with a character who is slowly being taken over by microscopic aliens. Since she is possessed, she is unable to overtly help the Doctor, but she discovers that she is able to obviously mislead him. They are thus able to escape, due to her saying things like: "There is not, I repeat NOT, a secret passageway hidden behind that bookshelf."
In the first The Kingdom Keepers book, Finn has to "borrow" something from the One Man's Dream museum in order to defeat Maleficent. When a cast member speaks to him, he quickly blurts out "I'm not doing anything wrong!" This, of course, makes her suspicious.
Ares: I am the god of war! I take orders from no one! I don't have dreams! Percy: Who said anything about dreams?
In the Dale Brown book Rogue Forces, Jon Masters is insistent that the XC-57 Loser is not a bomber, that the Slingshot laser is not an offensive tool and that the belly hatch is not a bomb bay. Subverted in that while the Slingshot does get used offensively later on, the Loser does not get used in a bombing capacity.
This trope describes all but the first paragraph of the back cover blurb of Of the City of the Saved ... and extends into the "about the series" section:
Of the City of the Saved ... is not a novel of violence and political intrigue, set against the backdrop of humanity's last resting-place. There is no evidence that it is the second in the series of original Faction Paradox novels.
"Here," said Wobbler suspiciously. "This is time travel, right? Do you know something horrible?" [...] "What, us? We don't know a thing," said Johnny miserably. "Especially about burgers," said Bigmac.
In Catch-22, when Colonel Cathcart discusses holding prayer meetings in the officer's briefings with the chaplain, he's resistant to the idea of letting the enlisted men join in, but NOT because he regards them as dirty, common and inferior.
In On Basilisk Station, Honor asks her bosun to look for people who "would be intimately familiar with the best way to hide contraband". When she is asked about looking for smugglers to man customs flights, her response is ... telling.
"Of course not, Major. This is a Queen's ship. What would we be doing with smugglers on board?"
In Dirk Gently's Holistic Detective Agency, Dirk apparently managed to attract a following at university thanks to the bizarre rumours he was constantly denying — although no one ever heard these rumours in any other context.
Diana Wynne Jones's short story "The Master" has many, many of these, all perpetrated by the character Eggs. Any question which he answers with "I don't not know" ... you probably want to re-phrase.
The Gaunt's Ghosts novel Blood Pact has a variant: Mabbon tries to hide the group from the Chaos witch by putting blood wards on Jaume's house so she cannot see that they are there. However, the witch casts her Blood Magic and zooms in on the curious spot that just so happens to be unreadable by her.
In The Va Dinci Cod, a parody of The Da Vinci Code, Robert Donglan is accused of the murder of Jacques Sauna-Lurker. The evidence: a three-foot codfish which has his fingerprints on every single scale. His defence:
'I never so much as touched this fish. I certainly didn't – handle – it, certainly didn't paw it over and over,' he shuddered, 'like some disgusting fish-pervert, like somebody who couldn't help himself, who just had to press his fingers into the soggy, firm, cod-smelling flesh again and again, as if he were kneading bread, touching it, caressing it, forcing it through my fingers like a potter moulding clay, throttling its silvery-shiny wetness, its fishy firmness, pressing it again and again and again, slapping it, faster and faster shouting out "bad fish! bad fish!" at the top of my voice, until losing myself in a foul conniption fit of ecstasy.' He wiped a small quantity of spittle from the edge of his mouth with his sleeve. 'I didn't do anything like that. I hope you believe me?'
During a meeting under truce with Damodara, Belisarius asks for a few moments alone with Narses, the Byzantine traitor now working for the Malwa. When Damodara questions whether that would be something a sane man would allow, Belisarius makes an oath that what he wants to talk to Narses about will not threaten Damodara. After the meeting, Damodara realizes that Belisarius denied planning to harm him personally. He didn't mention anything about the Malwa Empire.
Damodara later uses this himself. When Narses discusses a course of action (based on his conversation with Belisarius), Damodara very specifically denies giving him any permission to do such a thing. As Narses notes later, there's a difference between not giving someone permission to do something and ordering them not to do something.
The beginning of H.P. Lovecraft's "The Haunter in the Dark" consists of a couple paragraphs explaining that the general consensus is that Robert Blake was killed by lightning. Sure, the window was closed, but maybe lightning can do that. And the expression on his face was probably just because of a muscle spasm, not anything he saw. His diary entries were just based on local legends (sure, he also said he didn't know anything about them, but who believes that?), and the deserted church was obviously vandalized by pranksters with whom he was somehow connected. The well-respected doctor who read Blake's diaries and subsequently broke into the church, grabbed the stone and the metal box from out of the windowless black steeple and dumped them in the bay was just a crazy fanatic. Clearly.
And I will establish my covenant with you; neither shall all flesh be cut off any more by the waters of a flood; neither shall there anymore be a flood to destroy the earth.
The puppeteer leader of one of the Ringworld missions takes pains to explain that his ship carries no weapons whatsoever, only tools. He then takes equal pains to explain the safety precautions that must be taken when using each of the tools, which could be incredibly lethal if used improperly.
In The Dresden Files novel, "Ghost Story", Dresden gives one to the readers: "'Grenades!' I ordered, in a firm and manly tone that did not sound at all like a panicked fourteen-year-old."
In Cold Days, he has another one: "I didn't look at what that motion did to her chest, because that would have been grotesquely inappropriate, regardless of how fascinating the resulting contours may or may not have been."
In "Turn Coat", this trope crosses over with Could Say It But in that Morgan gives a knee-jerk denial to the notion of there being a traitor in the white council. It sounds so rehearsed that Harry is immediately clued into the fact that the denier already knew but is keeping mum because of the potential backlash.
I Want My Hat Back: "Have you seen my hat?" "No. Why are you asking me. I haven't seen it. I haven't seen any hats anywhere. I would not steal a hat. Don't ask me any more questions."
Enforced in Gelsomino in Land of Liars. The backstory explains that when the current military junta took over the government, they forbade speaking the truth - completely. After a while, the citizens (at least the braver ones) adapted and now they are talking only in such denials - i.e. "I am not going to theatre" means exactly the opposite. The people now understand each other quite well, while the effect on a stranger is devastating.
When Tash Arranda meets Luke Skywalker in Galaxy of Fear: Eaten Alive, she feels strange in a good way. She's unusually comfortable around him, and yet feels shy at the same time. In the narration she quickly states that it is not a crush, she has outgrown crushes.
William George (Billy) Bunter from the stories by Frank Richards (one of over two dozen pen names used by Charles Hamilton) lives and breathes this trope. "I never took the cake, and I didn't go up to the box room to hide while I ate it, and there were hardly any plums in it anyway."
In Atlas Shrugged, the controlled press runs stories like this; for example, "It is not true that the Miller Steel Company has gone out of business".
Three of the mothers of The Ultra Violets try and fail to disprove the existence of Helitropium.
David: I'm not going to question your journalistic integrity...
Shaun: Hey, Rick, ever notice assholes only say that when they're about to question your journalistic integrity?
Everyone in The Riftwar Cycle knows that there is no such organization as the Keshian Intelligence Service.
In 'The Reeve's Tale' by Margaret Frazer (set in 15th-century England), a teenage boy is explaining to the village reeve how he happened to be in a position to see a plot-critical event (note that the land belongs to a noble, and commoners aren't allowed to hunt there):
Dickon: There's a place up on the wood edge. It ridges out some and you can see...
Simon: I know the place. Every boy knows it. It's the best place along the woodshore for not catching rabbits. My grandfather used to not snare rabbits up there, too. And my father and me. None of us ever used to set snares there when we were your age, nor eat the rabbits we never caught neither.