There may have been crashes. But looking at those videos, and others, I have difficulty believing that one has been "shot down." Supposedly they're capable of maneuvers impossible for our best aircraft - like right-angle turns, instantaneous acceleration/deceleration, and the incredible speeds you spoke of.
I've been sure of alien visitation for a long time - I saw a flying saucer when I was a kid, and I'm not prone to hallucinations, and have always been able to distinguish fantasy and reality.
It's DAMNED mind-boggling.
Those things are REAL - too many sane, honest people have seen things that would be impossible with any technology we have.