Same thing they do with JFK. I have never seen a CT produce a start to finish narrative of what they think happened. All they do is poke holes in the Official Story. Which can be done to any historical event.
And the same sort of thing creationists do with evolution. For the CTers like CM and the folks at CluesForum, there is no real evidenced narrative (or need for one), only "a conspiracy diddit!" For the creationist, there is no evidenced narrative of natural history (and, again, no need for one) beyond "goddidit!" In either case, their idea of parsimonious explanation is to boil things down to a simplicity that they can accept and/or understand, and to try to poke holes in what they can't get and don't want to see. In both cases, they're missing the concept of "consilience of evidence" anyway.
And in both cases, the need for positive evidence is answered by an invocation of magical thinking; the conspiracy (or the deity) is simply assumed to have whatever properties it needs to
be a successful conspiracy (or deity). Asking for the nuts-and-bolts of exactly
how the gov't pulled off 9/11 or Newtown gets you "they're the gummint, man! They can do
anything!" (Though, apparently, not competently enough that the deceptions can't be easily spotted by Fearless Internet Detectives in Mom's basement) Trying to pin creationists down on the mechanics of "Creation" results, sooner or later, in "he's
God, man! He can do
anything!"
The CTers have a word they like to use a lot- "perps." I suggest that, in any given creationist argument, you can replace the word "god" with "the perps," and see the same sort of circular thinking.
This is a bit of rant; it verges on being off-topic, and I apologize for it. It's just that, having read this and other CT and creationist threads here on JREF, I've finally realized that CTers and creationists irritate me for exactly the same reason- when they need it, they use magical thinking, which by definition is without limits and irrational, as if it's a perfectly reasonable argument within the limits of what's real, rational., and evidenced. It's their get-out-of-jail-free card, one they use in a sort of bait-and-switch tactic when they realize that they don't actually have any evidence to support the conclusion they began with anyway. If someone is going to, at some point, need to invoke magical thinking to support what they want to believe, why not at least be honest and begin with it? I won't argue with faith honestly presented.