One of our air to air missiles would have taken the entire engine and part of the wing.the plane would have fallen at no more than about 300mph.
The plane hit at a very high rate of speed. Something a damaged plane with a missing engine could not possible have done. And there was no indication from passengers that anything like that occurred. Also, if we had shot it down, don't you think that we would have acknowledged it since orders had been given to do exactly that.
In point of fact, we actually failed to shoot it down before it crashed and the defense dept. got criticized for that as well.