Not entirely true (and not that ATC was trying to deviate anyone in this case), but the FAA can go after a military member's civilian certificate if they know the pilot's name/details. Essentially it's a dual jeopardy situation. However the FAA knows this and is fine with letting a member hide behind military protection. Hence why on a flight plan (back when you filed with a FSS regularly) you could just say "On file, KNxx" when they asked for the pilot's name.
Is there more to this story? Not trying to be a dick, I'm very curious as to whether they have been successful doing this to someone.
I got the advice early on that if I ever got a number to call, only ID yourself by your flight's callsign, and then call dad to let him know that the FAA may call someone.
With the VMU we've had a couple of folks do some wonky stuff, and a couple of airplanes do even wonkier stuff, and ATC got mad. Our response* to them was that the aircrew is doing something that the FAA doesn't have a certificate for, so they can pound sand. But then we did the FFPB thing when it was appropriate.
*Through the DCA's office, as in the cases of flight violations, technically it is the service chief who is the one who is supposed to deal with it. They delegate that down to the DCA office, and I'm sure it's the FAA liaison dude for the service that deals with the stuff.