If a physician is surprised in his home by three crack-crazed home-invaders intent on tearing him limb from limb and raping his wife and daughters, his traditional oath has absolutely no bearing on his right (nay, his DUTY) to employ his faithful shotgun.
He is saving life in that case and here, as well, though without any direct action on his part. His medical care for our troops means that they will prevent these Quran-crazed loonies from continuing to kill others.
You might as well argue that any physician who treats a law enforcement officer is violating the Hippocratic oath, because said LEO might shoot a burglar.
I can't speak for any branch of service except the Marine Corps, but I suspect all branches are the same in that respect.
The goal is always the same - killing the enemy - whether it's by changing a track on an M1 Abrams or treating a shrapnel wound on a squad leader's arm.
If he has earned his globe and anchor, his duty, FIRST, is to kill the enemy by whatever means given to him.