Ever watched one of those conspiracy theory documentaries and thought it made a whole lot of sense? I remember once watching a Fake Moon Landing documentary that pointed out the photos had two shadows. This initially seemed like a compelling argument for the film studio hypothesis, but more thought revealed that of course there were two shadows; one of them from the sun and other other from Earth, which is, of course, larger in the moon's sky than the moon is in ours.
It seems our beliefs are just as easy to fool as our eyes!