That being said, if the symbol was being used as the emblem of an evil army or crime syndicate in a game, I could understand them having a problem with it, however.
Part of the point of the symbol is to indicate the International Red Cross and Red Crescent Movement, specifically, which keeps to strict neutrality in wartime. If it starts getting used willy-nilly it puts their members at greater risk because they are no longer clearly delineated from the medical services or army medics of specific countries.