Hmm... legalese...
In former Soviet Union the emblem of "Red Cross on white background" was (and still is) widely used. 150+ millions of people easily recognize "RC on WB" as "something healthcare/medical related", but these people may have difficulties in recognizing the "red diamond" or "green cross".
I don't know if onboard medikits in European or American cars are marked with something other than "RC on WB", but here, in Russia and most of ex-SU these medikits are clearly marked with "RC on WB" - even illiterate person could understand.
BTW, how about "snake and shaft" or "snake and cup" emblems? The first, as I heard, is the sign of US "medicina militaris", and the latter is the emblem of Soviet/Russian military medics.