Yep. That's why "loyalty cards" exist. Since they're not allowed to associate your purchases (or really any data) with your CC number to build a profile they give you a separate ID number that you key-in/scan when you buy things.

"Oh but you don't have to use your loyalty card."

Technically true but it's not "get a discount if you use your loyalty card" it's now "pay really inflated prices if you don't."