Fimbul
You're not right in your assumptions. The red cross on white background is a protection symbol and therefore protected by international law. Any misuse of that sign is forbidden and is a punishable offense.
The use of the sign is only allowed for certain organizations and groups of people and only in armed conflicts. Anything other is a misuse.
The purpose of a protection sign, btw., is to be as simple as possible, so anyone can recognize it anywhere without further informations.
The countries around the world have different punishments for the misuse. For example, in germany it is a petty offense, punished with a maximum of 250,000.00� or 6 month of "Beugungshaft" (there seems to be no equivalent word in english, basically you're going to jail until you either pay your penalty or the time is over).
So don't take it too easy. Also ethically it is good manor to treat such protection signs with respect. (There are quite a few others, like the red crescent, the red lion, the blue triangle on orange background, the emblem of the UN, the letters "UN", etc.)