Correct. You're under no legal obligation to show the merchant your ID, so the 4th Ammendment doesn't apply. They may, however, refuse to do business with you.
Businesses have a very wide latitude over the conditions they can put on a sale, and over refusing service. Note the cases at WalMart and Best Buy where they banned people who were writing down prices.
The health department license had expired, and they couldn't find the current one.
I got a certificate for a gratis meal for two.
Uh, I'd wonder if there was a
reason they didn't have a valid inspection certificate. I'm not sure a free meal there was a great deal.