Ever since the term "Flying Saucers" was first used in 1947, there have been literally thousands of reported sightings and/or encounters. The problem is that, in more than 60 years, there has yet to be a single example of compelling proof.
When scientists see such a pattern - lots of stories but no legitimate evidence - they classify it as an anecdotal account.
A while back, I read a book detailing the ten best cases for UFOs being Flying Saucers...and believe me when I say that few things would excite me more than visitors from space. Yet, despite my personal preference, I can only say that the ten cases were interesting enough to attract a publisher but not one was airtight and nothing less will do when arguing that creatures from another planet traveled light-years to get here.
Police tend to discount eyewitness testimony knowing that it is usually the weakest link between a crime and the criminal. That's why so many new TV cop shows stress laboratory procedures that involve such things as rug fibers, pollen samples and blood smears. Not as satisfying as a victim getting to point out the felon in a lineup but certainly a lot more reliable.
Psychology professors will sometimes resort to classroom theatrics as a means of showing students how easily they can be fooled. In a classic example, a woman rushes in with a toy gun, aims it at the lecturer (who falls to the floor) and then rushes out. The understandably shaken group is calmed down, told they are part of an experiment and asked to give a brief summary of what just happened. Most will report having heard a shot, many identify the culprit as a man and a few will swear there was a knife. So much for what people say they saw.
Even pilots with many hours in the sky can be fooled. Once, while flying over a city at night, the air traffic controller told me to look for another plane approaching on my right. A quick glance and I had his flashing strobe in sight. A couple of minutes later, I realized I'd been watching the rotating roof light of an emergency vehicle on the ground 5,000 feet below. Seeing something usual in an unusual way can befuddle even seasoned observers. On another occasion, also at night, an enormous craft still off in the distance suddenly began closing at an enormous rate of speed. My companion, a former test pilot, was equally fooled by what turned out to be not one huge UFO but two regular sized helicopters that passed harmlessly to either side of us.