No, they’re allowed. I usually shop at Ralphs, and I use my card (I never have it with me, so I type in my wife’s phone number). On rare occasions, I have to go to Vons (like if I want to rent a Rug Doctor or something, and I end up buying more stuff while I’m there), and since I don’t have a Vons or Pavilions card, I end up paying full price. Not once has a Vons cashier offered to swipe a store card for me.
