Note that this isn't normal copyright, the red cross is protected under the Geneva Conventions
https://en.wikipedia.org/wiki/Emblems_of_the_International_R...
A green cross would confuse people.
Army medics != Red cross, and that's a big difference.
If a red cross is taken to mean just army medics, they might be considered to be "just" the enemy's medics, a "legitimate" target for some, unlike the Red Cross who are neutral and help everyone.