The Air Force recently (about 3 years ago) changed rules that allows Flight Surgeons to issue 3rd class physicals. Not any good for an airline guy.
SOME (very few) flight surgeons are authorized to be AMEs; ie, can give 1st-Class. A handful more can do 2nds, but not 1st.
I asked one of the few who could do 1sts, before he left my base: "Why doesn't the FAA allow military physicals---which are
far more stringent than any FAA physical I've ever taken---be allowed as 1st-Class?"
He said: "Secret handshake between the FAA and AMEs for job-protection. Like every raw deal in life---politics."