For the Good of the Outfit - S2-E4
Revealing mistake: Frank is shaving; when he bends down to pick up the envelope containing shrapnel fragments, the foam on his face and ear suddenly all dries up. The shot must have needed a lot of takes. (00:07:20)
Answer: Even an Army field hospital would have SOME weapons for self-defense if the enemy attacked. What's meant is that it's not a combat outfit, and therefore wouldn't have enough weapons to actually attack anyone. (It's also mentioned a few times that the Officer of the Watch is supposed to carry a pistol at all times, but Hawkeye refuses to do it when he's in charge and Colonels Blake and Potter don't enforce the rule).
Captain Defenestrator