Advice and Trust: The title references Misato advicing Shinji to trust his feelings and ask Asuka out. That happened in the first chapter -the history was supposed to be an one-shot-. It has been a bunch of chapters since -and Shinji and Asuka got together long ago, so the title does not describe the fic any more.
Digimonfanfiction tends to have this problem (i.e lots of the human characters, no Digimon and if you get the Digimon, there's a decent chance there won't be any villains to battle). This is because Digimon has a LOT of fanfiction, and fanfiction is primarily a medium for the writers' romantic fantasies. Those selfsame fans complained when Frontier didn't have any Digimon partners and instead focused on the human team dynamics.
A lot of Pokémon fanfics either don't include Pokemon or barely mention them.
A lot of Harry Potter fanfiction features no appearance by the title character at all. In fact, there is a whole genre of fics dedicated to the era when Harry's parents attended Hogwarts. There's also plenty of fics about the early days of Hogwarts, taking place long before any of the characters from the books (except a few of the ghosts) were even born.
Likewise, a large percentage of Fullmetal Alchemist fanfiction does not actually include Edward Elric, the titular Fullmetal Alchemist.
And by definition, any fanfiction taking place after the manga's ending doesn't include the Fullmetal Alchemist, because Ed is no longer an alchemist.
For that matter, the same logic also applies to the 2003 anime'smovieConqueror of Shamballa.
The Land Before Time features many fanfics involving time travel to the future... so... not set in the land before time then...
Most popular Rave Master fanfiction contains no reference to the rave stones at all. The biggest ones, in fact, are the ones where the characters are set in a normal universe with no magic or swordfighting of any sort.
Calvin and Hobbes: The Series has "The Transmitter Conspiracy", which reveals the so-called "conspiracy" behind the transmitter, then proceeds to go into a plot that, while still based around the transmitter, doesn't really have to do with the conspiracy.
While competition fics are common, there's a large amount of Total Drama fanfiction that deals with the characters in situations that aren't a part of competing. The most notable of these would be High School AUs, as well as any story which is set in Playa des Losers or has its focus on a character's Backstory rather than their time in the game.
Any Teen Titans fanfic that isn't about the Titans, or ages them up so that they aren't teenagers any more.
If a Vampire Academy fanfic is set in an All-Human AU, it becomes this by default.
Yu-Gi-Oh!'s title can refer to three things: Yugi (the protagonist), his alter-ego Atem, often named the King of Games, or just the concept of a character who could be considered a King of games. Plenty of fanfics feature no Yugi, no Atem, and no games of any kind.
Meg's Boyfriend: While the titular Zack does become Meg's boyfriend, they actually get married early on right before their the birth of their daughter. Averted with the two sequels, Meg's Family and Meg's Family Returns.
The Elemental Chess Trilogy is still known by that title, even though it's now a Fan Verse spreading across the original trilogy, a prequel, a distant sequel about the Spinoff Babies, and a collection of side stories that didn't really fit anywhere else.
The first story of the Gensokyo 20XX series took place or, rather, it started in Gensokyo. The rest of the series, save sidestories, do not.
Intercom is this according to Word of God. The plot is started by an intercom system being accidentally damaged, but it isn't really central enough to justify naming the story after it.