For whatever reason, honestly and firmly believing what you argue seems to be a fundamental requirement in a critical discussion. On account of this, a key challenge to an opponent is that not even she really believe what she's saying. It's a kind of (non-fallacious) ad hominem scheme: "you don't believe what you're saying, so I'm not going to waste time with you." Basically, it's an accusation of trolling. Enter O'Reilly and Trump (via the Huffington Post–sorry, boycotting New York Times' pay wall):
O'Reilly said his show had looked into the claims about Obama's birth certificate. Once they found the two Honolulu newspapers which announced his birth, he said he "put [the issue] to bed," since "that is impossible to make happen" if Obama was not born in a Honolulu hospital. O'Reilly labeled Obama's mother a "hippie," and scoffed at the notion that there was a "sophisticated conspiracy" to smuggle Obama into the U.S. and forge his identity.
"What is he, baby Jesus?" he joked. Trump said that he remained convinced that there was something fishy going on. "People have birth certificates," he said. "He doesn't have one." He then repeated the speculation that had so angered Whoopi Goldberg—that something on the birth certificate must be so radioactive that Obama is covering it up. "Maybe it says he's a Muslim, I don't know," Trump said. "…If he wasn't born in this country, it's one of the great scams of this time."
O'Reilly finally said he didn't believe that Trump was serious in his skepticism. "It's provocative, I think it gets a lot of attention, but I don't think you believe it," he said.
This is an obviously legitimate employment of it–good for you Bill O'Reilly–but I wonder what you'd call the illegitimate use–should we just call it "trolling." How might we identify it? What might be the scheme?
UPDATE. Can't believe I forgot the recent revelation from a Fox News personality that he advocated for an idea he found "privately" to be "far-fetched". I guess he did it for the lulz.