It could be problematic, though. Research* indicates some kinds of gullibility are strongly biased towards believing in shadowy groups, rather than being equal-opportunity stupid. Subjects will seize upon anything they perceive as evidence of mysterious conspiracies, while completely disregarding evidence against regardless of strength.
Although I suppose there's not much point to being the Illuminati if you don't occasionally orchestrate a murder of someone who discovered your secret. Just to keep sharp.
*by which I mean "a passing familiarity with internet crackpots".