The aspect of Batman that comes to mind in regards to conspiracy theories is his Rogue's Gallery; or more specifically, the MO of The Riddler. Over and over, it seems these thousand-year old super-secret ruling cabals of everything just can't stop themselves from leaving labored and obvious clues strewn about the landscape.
I'd give the conspiracy believers more credit if they'd just follow their reasoning one more step. But I've never seen a one of them suggesting that the clues they find are traps, carefully designed to out the non-believer, ferret out those who can see the fnords, and thus aid in their location and eradication.
The absolute one thing the conspiracy can never do (well, besides go to the Moon), is to find some guy with a YouTube account and send the Men in Black to where he lives.