'I would think there is a fair amount of "covert" coordination between Mil flight ops and civil ATC.'
Ummm, you must be joking, the entertaining thing is that 80% + of a Mil flight in the ME theater is conducted in civil airspace and trust me we do
not conduct any liaison with the military authorities unless they come over and simply say "shkoomer" is not allowed through!
The reality is the less people involved the better, very similar to any organizational environment...