It can be worse than that sometimes. The crackpots see some nuggets of truth, and for whatever reason, they make some leap in interpreting them that leads them to nonsense. They keep finding things that are either true, and add them to their worldview, or made by people who took compatible leaps of logic away from reality. They propagate it to others.
Taking Kennedy’s assassination as a classic example: it’s true that a lot of people wanted him dead, some benefited from his death, the CIA has a history of assassinations, and Lee Harvey Oswald was a communist who had once lived in Minsk. I can see why someone with just enough information to feel confident can arrive at a belief that the CIA or USSR killed Kennedy, while missing critical information to realize there’s no reason to believe either is true.