This is simply not true! Have flown recently with other *A carriers, and my TK Elite (*G) STATUS was printed on my BP. I always hand them my *G physical card, and ask them to make sure that my FF# and my status is on my rez and my BP.
P.S. I seem to have read somewhere that SK did have some problems recognizing other carriers' *G status (for lounge access, priority bags/boarding/screening, etc.). Maybe it was a system glitch?! But I suppose a physical card should solve the problem?