I'm unconvinced by reasoning that assumes that once someone inside the conspiracy decides to talk, the conspiracy will be unmasked. People may not believe them,

I'm unconvinced by reasoning that assumes that once someone inside the conspiracy decides to talk, the conspiracy will be unmasked. People may not believe them, particularly if the members of the conspiracy are in a position to undermine them. For example, there are many conspiracy theories surrounding the death of Dag Hammarskjöld. Supposedly in later life Van Risseghem admitted that he shot down the plane. But this hasn't led to the case being resolved, because we don't know if it's true that he said that, and even if he did we don't know if he was telling the truth. Similarly, as I understand it, conspiracy theorists around the Kennedy assassination aren't short of statements, or reports of statements, by people who claim to have been in the know (for a number of mutually inconsistent theories, of course).