The OP's premise is absurd. One merely has to present a valid STARGold card to the receptionist. It doesn't matter what program it has been issued from nor which program you are crediting your flight(s). I have interchangeably used my AE, CO and UA STARGold cards when flying these various carriers and crediting my flights to a different program.
Last week I was flying some intraEurope flights on LH (in K class which only earns miles in M&M) and used my AE or CO or UA card to get into the Senator lounges, but was crediting these segments to M&M. No problems anywhere.