After reading something:
Did I read this right? Did that just say that it isn't one corporation's logo, but rather a symbol used under the Geneva Conventions to show for first aid and other medical related shit. Basically, having a medic class in a war game with a cross that happens to be red would be doing what the Geneva Conventions quote demonstrates, and isn't infringing on International Committee of the Red Cross's (lack of) ownership of it.
Except for, back in the tfc days, when players would go medic only for speed, self healing, concjumping, and never (or rarely) healing teammates