I think that a lot of these people, if they ask themselves, "could what I saw really only be explained by angels/aliens/Bigfoot/et cetera," in most of the cases, the answer is no, at least if they examine their own experiences objectively, and with an eye toward science and skepticism.
Like, say someone who is interested in Bigfoot is hiking in the northwest, and he sees a big, hulking upright primate figure about fifty meters away lumber off into the woods. The most likely and reasonable explanation is that he saw a person, but maybe he works it around in his mind, and becomes more and more convinced that it was a Sasquatch. I am not certain that he is delusional, but he certainly is probably not properly rationalizing his own experience. Human observational ability and human memory are quite fallible.