Claims of UFO interference with ICBMs

Some former USAF personnel have gone public with claims UFOs were able to take control of Minuteman ICBMs, or at least interfere with them. Here's why I think memories are playing tricks, or something.
Several people say things happened, but hundreds of thousands have served in ICBM units without reporting any such thing, and no official documents have leaked. UFO sightings? Sure, they've happened in missile fields (they are mainly of the nocturnal lights type, which often prove to be astronomical phenomena or aircraft lights magnified by unusual atmospheric conditions).
But taking control? I'm not at all convinced. In the first place, I don't think
it's physically possible. Even advanced aliens have the same laws of physics governing propagation of radio signals, etc. The capsules, buried several stories deep, are grounded and hardened against any type of interference (MIJI) or (much more powerful) EMP from a nuclear near miss. A beam of EM energy powerful enough to penetrate earth and shielding would have left physical traces, like melted insulation.
If it somehow happened anyway, the investigations would have been immediate and extensive, and they would have been followed by emergency control system modifications to increase resistance to interference. These actions couldn't have been kept to a small circle (granted, the brass would have tried to do that, but I'm pretty certain it wouldn't have worked).
Matt Bille (another former USAF ICBM officer)