In my experience, BPs printed at the Delta counter for codeshare flights show the Medallion status, but not those printed by some partners.
I carry my GM card in my wallet (though I've yet to receive my 2014 credentials), but always show my card in iPhone passbook. I did once have an AS BR agent ask me to show her the SC card directly in the app, because "that could be faked." In that instance I just pulled my SC card from my wallet.