It's pretty clear that most eyewitness accounts of observations with ordinary explanations is correct. What we are left with is a tiny minority of people who observed an ordinary event and concluded that it was an extraordinary event.
A tiny percentage of witnesses, multiplied by the large population and large number of ordinary events, yields a number roughly consistent with the numbers experienced.
Lights in a triangular formation is pretty typical for aircraft; each type has several different possible configurations of light, and almost all of them involve three or more lights that aren't in a line. Without anything to create perspective, it is basically impossible to tell the distance of an aircraft by eye even in the day (experienced people can identify the type, know the size, and do the trig to convert degrees of arc or elevation and altitude to distance, but those people typically recognize aircraft lights as aircraft lights).
Three lights in a triangular formation, perceived as distant and far apart and with no audible noise, is roughly what one would expect to experience if a Cessna Caravan was making a nonstandard approach to a nearby airport. If the airport lacks an operating control tower (like most municipal airports in the middle of the night), it is reasonable that air traffic never communicated with the aircraft. Further, it is perfectly legal for such an aircraft to fly without an installed transponder, meaning that the radar track (if observed) will show something there that cannot be proven to be an aircraft.
Think you don't have a municipal airport near a given witness? The US has about 13179 public and private use airfields, roughly one for every 300 square miles.
Recently I've been struck with a belief in Aliens being present on this Earth. It happened after I watched this documenary (and subsequently several others). My feeling of belief is not particular interesting in itself - I could be lunatic or otherwise psychological dysfunctional. What I'm interested in knowing is to what extend other people, who consider themselves rationalists, feel belief in the existence of aliens on this earth, after watching this documentary. Is anyone willing to try and watch it and then report back?
Another question arising in this matter is how to treat evidence of extraordinary things. Should one require 'extraordinary evidence for extraordinary claims'? I somehow feel that this notion is misguided - it discriminates evidence prior to observation. That is not the right time to start discriminating. At most we should ascribe a prior probability of zero and then do some Bayesian updating to get a posterior. Hmm, if no one has seen a black swan and some bayesian thinking person then sees a black swan a) in the distance or b) up front, what will his a posterior probability of the existence of black swans then be?