I wrote one back in high school that I still trot out every once in awhile:
Magic Johnson doesn't have HIV. He never did. In 1991-92, AmFAR was trying to find a good way to raise a lot of money through donations but kept running into the problem of having the public think "AIDS only happens to gays or drug addicts or people in Africa." Meanwhile, Magic Johnson was having trouble at home---his wife had caught him sleeping around and was threatening divorce, so he had to find a way to convince her that he'd changed his ways.
Meanwhile, Magic was only making $2.5 million with the Lakers, making him only the 21st highest-paid player in the NBA that year and not even the highest-paid player on his own team (source [http://www.eskimo.com/~pbender/misc/salaries92.txt]). He was also in his 12th year in the league, he was 32 years old and suffering the effects of a knee injury that would keep him in limited action during the season and upcoming 1992 Olympics, and he was in a position where he'd be receptive to pursuing other avenues in life while still at the height of his popularity in Los Angeles.
Enter AmFAR. They knew they'd get so much in donations that they made a secret backroom deal with Johnson that would pay him a cut far in excess of his remaining salary potential in the league. All he had to do was take the fall and claim he'd contracted HIV from his many sexual conquests. Since he'd be radioactive to women, his wife would feel better about his fidelity, and since he could turn around and use his "status" to educate kids about the dangers of the disease, he'd be seen as a "hero" and "courageous" and all that other Oprah crap that was starting to become popular in the early 1990s.
Suspicious facts? Well, Magic must've had unprotected sex dozens of times with his wife Cookie, and she was pregnant with his child at the time of the announcement. The drug therapies that prevented transmission from mother to child were still in their infancy (no pun intended), so by all accounts mother and child alike should've contracted the disease, right? Except they didn't.
Meanwhile, in a later 1996 interview, Magic credited drug therapy with "curing" the disease when he had his viral load lowered. Anyone who's ever been around HIV-positive people knows that "Cure" is a word you NEVER hear them say. "Manage", yes. "The drugs are a miracle", sure. But "cure"? Never happens.
So therefore, Magic Johnson does not have HIV. He never had HIV. And the whole ruse continues, paid for by a combination of that upfront funding from AmFAR and the later need for Johnson to go along with the conspiracy because to reveal otherwise would cost him tens of millions of dollars in lost value in his personal investments when his reputation got murdered.
(note that I don't actually believe any of this. Wrote it to prove a point that some people will believe anything---hell, some people bit on that nuclear explosion Mythbusters thing I wrote for April Fool's Day!)