That doesn't change anything. My best friend was a paratrooper in the opening invasion of Iraq. You can call people by their specialties for shorthand, and it doesn't mean they don't have other qualifications. I mean, of course you would. You'd say "get me the medic," not "get me the medic who is also an adept soldier, spy, etc."
Are you seriously suggesting that because he's called "the medic" that's all he can be? He's dressed like a rank-and-file soldier and is the only MSF member outside of Morpho who is accompanying Boss on his mission. He's not just some nobody. (In terms of skill set, I mean. Of course he's a blank slate as a character.)