Where There's a Will, There's a War - S10-E16
Revealing mistake: When Hawkeye injects the adrenalin into the chest of the dying soldier at the battalion Aid Station, you can see that he is actually injecting into a piece of rubber foam soaked with prop blood. (00:13:25)
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