If you think "how to get into OMFS" is a secretive process in general, military OMFS must be fairy tales because we never hear anything about it. From what I know about military OMFS through externships are the following:
1) they only pay/offer 4-year OMFS training (if you want the MD, then you're on your own), but the official military residency programs are all 4-year programs
2) there are roughly 20 official OMFS military spots (@ military medical centers) between the three branches (Army, Navy, and Airforce), but some regular OMFS programs offer spots to military applicants such as Minnesota, LSU NO, and Houston (again, they're all 4-year guys)
3) all official military OMFS spots at military medical centers do not participate in MATCH, but if a military OMFS applicant want to be trained at a civilian OMFS residency program, then (s)he must participate in MATCH
I believe even in military OMFS residency programs at military medical centers, they absolutely train in General Surgery.