2) Use of the Greek red cross other than by the American This quote is from bitlaw.com, statutory protection.
"National Red Cross is proscribed by statute. 18 U.S.C. §706. Use of the coat of arms of the Swiss Confederation for trade or commercial purposes is proscribed by statute. 18 U.S.C. §708. See In re Health Maintenance Organizations, Inc., 188 USPQ 473 (TTAB 1975) (mark comprising a dark cross with legs of equal length on which a caduceus is symmetrically imposed (representation of caduceus disclaimed) held registrable, the Board finding the mark readily distinguishable from the Greek red cross (on white background) andthe Swiss confederation coat of arms (white cross on red background...

2) Use of the Greek red cross other than by the American This quote is from bitlaw.com, statutory protection.
"National Red Cross is proscribed by statute. 18 U.S.C. §706. Use of the coat of arms of the Swiss Confederation for trade or commercial purposes is proscribed by statute. 18 U.S.C. §708. See In re Health Maintenance Organizations, Inc., 188 USPQ 473 (TTAB 1975) (mark comprising a dark cross with legs of equal length on which a caduceus is symmetrically imposed (representation of caduceus disclaimed) held registrable, the Board finding the mark readily distinguishable from the Greek red cross (on white background) andthe Swiss confederation coat of arms (white cross on red background))."
There was also a case from the 1990's where a multiblade knife made in China, with the Swiss shield and cross and the words "Swiss Army Knife", was ruled as a violation of trademark regs. That's all I can figure, anyway. Hope this helps.