I've seen plenty of things which, had I believed that my unaided perceptions alone were sufficient to reach a conclusion, would have led me to believe something that wasn't true. That it's possible for someone to saw himself in half and put himself back together again, for example.
Fortunately we usually have a plentiful supply of objective evidence to check our perceptions, and hence those conclusions, against. Where we don't is when we tend most often to be wrong, which we frequently are.
Unaided perceptions aren't entirely the same as firsthand experiences. An experience is the sum total of your perceptual, cognitive, emotional and intuitive functions. For example even though you witnessed a magic act, you know it was an intentional illusion, so you didn't draw the conclusion that someone was actually sawn in two. Also, although we have a lot of objective evidence for many things, the vast majority of the time a scientific verification of those things isn't necessary for us to make valid decisions. We perform thousands of actions in fluid succession daily based on our firsthand experience without verifying everything first. Simply because something unfamiliar comes into the picture doesn't mean we automatically screw up every time, especially if we are trained not to screw up and are expecting it to happen, as in the case of Air Force pilots who are scrambled after unidentified radar targets. Or in the case of my own sighting because I watched the object land I knew it had to come up again, so I waited and watched for it in order to get a better look and it appeared as anticipated, more than once.
The other issue is that of "unaided perception". Unaided perception gives us direct sensory exposure to the objective reality while a machine filters the stimulus through a mechanism that is capable of error. For example some people who claimed to have seen UFOs on their video cameras were actually watching an effect produced by the lens iris at high magnification. Telescopes or binoculars are relatively safe but still subject to prismatic flaws and lens flares. So assuming the witness has normal healthy sensory function, aided perception although often useful, also introduces another possibility for error into the observation.
Lastly, our firsthand experiences are not always scientifically verifiable, but that doesn't mean they aren't real. As emotional creatures we also sense things in ways that aren't easily measurable. Sure we can hook ourselves up to a brain and body scanner, but the readouts don't relay our emotions or our intuition, they merely reflect them in measurements of physiological states that happen to coincide with them. So we can't objectively prove they are real, yet our emotional state is a very real and meaningful part of our daily experience and overall mental health.
Now all that being said, I've experienced sensory illusions several times and experienced what seemed like valid intuitive responses to seemingly spooky situations that upon further investigation turned out to have perfectly logical explanations. So it is certainly important to consider as many alternative rational mundane explanations as possible that fit the situation. Where I find the skeptics going overboard is when they start changing the elements of the story to fit their mundane explanations, or go further to accuse witnesses of doing the reverse, which although can and probably does happen, isn't justified without some further rationale gained by investigation and study. In other words, it's possible to remain skeptical of a report without automatically assuming the witness was fabricating the story.