The part in bold is not accurate to the three store chains in my area of Massachusetts, namely Stop 'n' Shop, Shaw's, and Hannaford's, the last of which doesn't use such cards, and has been advertising with the slogan, "no card games!"
The point about the cards is that it allows them to mark things as discounted when they aren't. You jack up the price a bit, then add a "special card discount" to lower it again. If the customer believes that he or she is getting a deal, he or she is more inclined to buy. And because that "deal" is dependent on loyalty, the customer is less likely to notice the trick because he or she isn't comparing to other stores.
A local market survey group did a 3-month survey and found that prices at Hannaford's were on average lower for essentially everything than at the other two stores, even with the "special card discounts"; without these, the difference was ludicrous. Interestingly, some of the things that were most consistently cheaper at Hannaford's were the things most consistently card-discounted at the other stores. Translation: if it gets card-discounted often, it's overpriced even at the discount.
So when I left the US in June, at least in Massachusetts, the loyalty cards were completely dishonest. People should be able to figure it out themselves, really: have you ever gone to the checkout and forgotten to bring your card? They have one at the register and beep it for you as "customer service." In other words, unless the cashier is obnoxious (or you are), you always get the "loyalty" discount. Shouldn't that be suspicious, something for nothing, a big corporation just giving things away?