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...
I've literally used them when developing a video game before, and that's what I was thinking as I implemented them.
I've also used the red cross when making a game before without even thinking about a possible trademark or protection, it was already a generic symbol to me. Come to think of it, I just used it again in the art for a board game I was making. I guess I should change it, but I'm not sure to what (I guess a green cross?).