Semantics
USMC:
"Civilian Flying" on a miiltary medical = flying a General Aviation aircraft, not for hire.
So, you could use your mil medical = 3rd class to take the family someplace in a C-172.
The irony is, every military medical I've ever had was much more thorough than the civilian counterpart.
According to both a Navy and an Air Force Flight Doc I've spoken with on the subject, it is purely political. A secret-handshake between the Pentagon and FAA...."protecting" the job security of the MEs who do Class 1s and 2s.