Yes this is true. Without a player's card, Bally's will limit you to 1x$200; Hard Rock to 1x$100; even in PA, Valley Forge will limit you to 1x$100 if my memory is ok. Other clubs in AC like Ocean implement limitations too. A bunch of morons.
I don't have the answer to the question, but if I know the dealer is using a selective up card method, I would simply not play.
Knowing the exact answer to your question might be VERY interesting...