It's about the ubiquity in fiction. If every police box in fiction was a time machine, it stands to reason someone may be confused when encountering a real police box for the first time.

The misuse of the red cross, especially in video games, is rampant to the point that the Red Cross is worried about confusion.

There's additional issue with the fact that video games are very common, but warzones and disaster areas less so. So it's quite possible the fictional association, if overused, could redefine the real-life usage for many people. We already see some of this in the comment section... many people don't understand the difference between "health" as a concept and the red cross as an element protected by international law.

It seems reasonable to try and claw that meaning back.