Most conspiracy theories start with a false premise to which logic is then applied -often correctly. A trivial example popular among geeky music lovers is that instruments and whole compositions sound better tuned to 432Hz rather than the more common 440Hz. Much effort i devoted to showing why 432 is more numerically interesting than 440, and since 99% of music is about the juxtaposition of numerically interesting frequency rations, the arguments are superficially quite convincing, especially from an aesthetic point of view.
Where it falls down is right at the beginning - not in the idea that 432 is an interesting number (it is) but in the idea that 432 cycles per second is important. People tend to forget that the second is a pretty arbitrary time division; we're just used to think about time as a fact because it is convenient in everyday life. Pro musicians and sound engineers are constantly thinking about frequencies to the quantity of a second comed to seem as real as the pull of earth's gravity to an aerospace engineer.
In my experience, the longer the argument between an initial false premise and the conclusion, the more firmly the proponent will resist attacks on the theory, perhaps because it has required a higher initial investment of work to validate all the logical steps.