Alien visitations are possible, but they haven't been proven, yet people believe in alien abductions, crystal power, q-ray braclets, and lots of other things that have not withstood scientific scrutiny. I've seen posters and T-Shirts with aliens on them with the saying "I want to believe" on them, which I think sums up their thought process nicely. They are biased towards believing in such things so they do, regardless of the facts that may present themselves, or the lack of facts/evidence to support such claims.
Since I mentioned Carl Sagan in my previous post, here he is talking about an alien abduction case in the PBS series Cosmos. This was made in 1979 so the production values aren't the best.