I think this is something floor personnel do when they're suspicious of your intentions but want to find out more about you to be sure. The usual scenario goes like this for me:
"Did you have a player's card?" (Knowing full well I don't)
"No"
"Do you want one?"
"No, thanks"
"Are you sure? You can just give me your ID and I'd make one out for you"
"No, that's all right"
"All I'd need is your ID"
"Um, no"
I've never had anyone push beyond that, nor have I ever felt "forced" to give them my ID.
EDIT: Oh, Snorky, it's you. If you're playing where you used to play, it's because the pit become instantly very suspicious of players without player's cards. I've begun to think they're actually instructed to do so. I only get my ID checked at the entrance by the security guard (they're instructed to check anyone that "looks under 35"). But with a player's card, they don't care. Hiding in plain sight, so to speak. If you're not playing where you used to play, then disregard this edit.