There are lots of secret military devices that even other military don't know about. They often have advanced technologies - like the stealth aircraft which are essentially invisible to radar. Many UFO sighting were of military rockets or aircraft that the military would deny having any activity in the area. The famous Roswell incident was one such early military balloon back in the late '40's.
What I would be extremely skeptical of is anyone, including experienced pilots, stating that the object appeared to violate the laws of physics! Remember Einstein first published his special theory of relativity (dealing with objects travelling near the speed of light) only a short time after the Wright Bros flew a few hundred feet at Kittyhawk. Arthur C. Clark said that a sufficiently advanced technology is indistinguishable from magic. Back when I was a student, we used photographic emulsions to capture very faint objects. Kodak had developed them for extremely low light cameras for the military and then when they were declassified, let astronomers use them. Someone told me at the time that if they had access to new emulsions (like those that took pictures of the missiles in Cuba in the early '60's, we could have much better photographs than what we could then have. Same with optical systems.
It is reasonably to assume the military would have interest in being able to have high speed missiles that appear to turn 90* on a dime. What better way to confuse those monitoring and that may or may not have missile defense?