Haha, that's funny. ;-) I wouldn't worry too too much about this in a soccer tournament. Oh, and I usually take good care of my stuff, I would never leave my bag unattended. The emergencies I take care of are not as important as yours.
Thinking of the star of life marking on bags again... my SAR team actually supplies large Ferno trauma bag on important events, I don't see why I couldn't have such a bag myself. It's just a first-aid bag, it doesn't really scream "I'M AN EMT!" don't it.
I looked at Plano tackle boxes in the meantime, some are nice but I presume not ideal for my needs.
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"The only easy day was yesterday."