Air Force, Navy and Marines can all wear the Parachutist Badge upon completion of Army Airborne training.
EDIT: He is wearing a Senior Parachutist Badge, which, unless I am wrong requires a couple of mass tactical full equipment and full equipment night jumps. Which the Air Force does not conduct. It could be done in one tour in an Army Airborne unit.
Not saying it isn't possible. I served with former Marines, Navy and Air Force personal while in the Army. That Master Sargent just seems to have a whole lot of "diversified" specialized training and awards for someone of his apparent age. Could be possible, but........