So if a shop signs up for the service, and on Monday morning they have one customer who comes into the shop and buys something ... then that customer goes to another shop and just browses. You'll likely have the name of the person because they paid by credit card. You'll also have the information that this customer went down the block to some other shop. And you'll know which customer it was because you only had one customer that day.

So tell me again how I can't use this information to identify who a specific individual is.