When I visited the school for my interview, I was told that residency spots are actually easier to get through the military. That's because the government already has spots saved for the military grads and so instead of competing against the nation for residency spots, you just compete against your class. Even within your class you only really compete against those that are enlisted in the same service as you...
For example, I've been accepted through the Air Force and so come residency time, I apply for the residency spots that Air Force has already saved for their people.
From what I hear from the grads and students, it's a great and low stress system. My premed advisor also says that the military has some of the best residencies in the country.