Consider inductive reasoning (or falsificationism or whatever). Broadly speaking, this operates off the principle that assuming the universe has uniformity can't do any harm, and may do some good.
There's a pathological case where this isn't true: where the universe is actively trying to make your life difficult. In that situation, the uniformity assumption is a death-trap. Just imagine trying to win a poker game by rigorous experimentation - you'd get 0wned.
The human brain has access to a different kind of rationality designed to handle these cases. It's a rationality aimed at (to quote Neal Stephenson) condensing fact from the vapour of nuance. It uses rules like "once accident, twice coincidence, three times enemy action". It's not rational in the usual sense - but, insofar as rationality is ultimately pragmatic, it has an equal claim to the title.
So in a sense you could say that conspiracy theorists aren't really irrational - they're just jumping the gun slightly by engaging this secondary mode of rationality before they know there's something there to be investigated. The problem is, of course, that once it's been engaged it can't be turned off. When later tests come back negative, that just means your enemy is even smarter than you thought.
Say my name
7 hours ago