Yikes, that's pretty horrific. I think I'll be paying with cash at these places from now on.
So when you return items, they will ask for your id, even if you paid cash originally.
Some stores simply require an ID for any and all refunds. The reason for this is fraud, actually: I worked at a retail pharmacy in the US, and we had a group of people that would look through the trash to find cash receipts. They would proceed to another store to steal the merchandise, and then to a third store to refund the item.
Nearly all stores require ID if you do not have a receipt and enter it in their system. It might not be your card, but it'll be tied to your name and ID.
These folks searched the trash cans. Got receipts out that said method of payment was cash, stole the item and "returned" it. Yet another scam is to take such receipts from the trash, buy the item at a discount, and then return it to a more expensive store.
Sure, the store can see the item was paid for by someone, and even see the store it was bought from. But it can't know if the person just found the receipt and is returning stolen goods or goods bought elsewhere so long as the barcode matches up.