There is a genuinely terrifying explanation that fits all of the data-points: That something about routine exposure to the physical effects of flying military jets effects a pilot's perceptual accuracy.

This is also definitely something that would be on the hush rota; if your seasoned missile operator just reported overtaking Santa's sleigh at Mach something, it wouldn't inspire much confidence in either the new recruits or the public.

Combine that with targeting systems that likely have a strong false-positive-bias and you have a recipe for Earth having been visited by little green men.