This is two tropes. One, as the title would suggest is denying something so specifically that the denial is technically true, though the truth is slightly different. The other as the page quote would suggest is denying something that no one was actually accusing you of, which adds suspicion unto yourself as one wonders why they'd deny that.

I've reinserted the “I'm not anti-Semitic, but...” phrase because it's an almost perfect mirror of the BNP's opening line. I know there are a lot more people who want to destroy Israel than support the BNP and I know many people like Mr. INH might not like being compared to them, but if we are going to have one then we should have the other too.

I'm not entirely certain that a lot of people understand the definition of a "denial"...

Is there a particular reason the self-demonstrating part of the trope was removed?

I just had quite the Swiss Moment when I saw what "A clown is a big spider..." was potholed to. :-D