Well, I'm not the one making the claim, and so I don't feel like proving a negative, but his shtick is pretty straightforward (for all the characters, with some variations):
1. Set up a fake interview or staged encounter.
2. Immediately confuse the interlocutor with completely unreal mannerisms/speech. People watching the movies maybe don't pick up on this because they're used to the behavior, but if Borat started talking to you, you'd immediately be thrown off center. A lot of people seem to be overly-polite and nodding because of this, and that's part of how he manipulates them. There was a guy who dressed up like Borat at the ocsars (or some award show) and Cohen was immediately in the same situation.
3. The character then either does one of two things:
3a. Says/does something extremely impolite. Examples include bringing shit to a dinner table, stripping in front of a congressman, singing fake anti-American anthems in front of a "white trash" audience, or singing about killing Jews at a redneck bar. None of this, as far as I can see, gets at any kind of "truth". When Ron Paul called him "queer" or whatever, they tried to make him into a "hater". Well, no. I would have called him worse things, and I'm pretty sure I don't hate "queers". The "Jew killing" song was set up by an hour of standup comedy by Cohen, and everyone knew it was a joke. Again, you know who's the liar in cases like that.
3b. By asking bizarre questions at fake interviews. There might be some instances where he got someone to admit something genuinely valuable, but I don't recall. It's clear he's just trying to make people look silly or trip over their tongues (Pat Buchanan talking about "Mustard gas on the BLTs") or admitting something ridiculous ("Are being racist against me because I'm black?"). I haven't seen as many of the interviews because he did that more on his British TV show, and I sure as hell don't spend my day surfing for them on youtube.
Anyway, his real purpose is to make the audience feel superior to somebody famous or somebody who represents a stereotype (whether rednecks or stuck-up UMC southerners, or Romanians, or whatever) by making those people metaphorically drop their pants in one way or another. Disagree or disagree that it's a bad thing, I don't care.