The shop staff suggested using a faked ID - but they didn't suggest that this should still be the persons only ID for Facebook. That was their solution as an individual.
They're not even particularly contrary as practical solutions go - the first policy is presented to the public, it works to reduce wifi abuse. The second "policy" is not presented and works to try and avoid confrontations.
Even if they put big signs out the front of their shop saying : "You can make a fake account and use our WiFi if you care about your privacy." Most people would not go through the trouble of making a fake account and just login with their real account.
The fact that the clerk was in conversation with this guy probably put him in the "non troublemaker" category in the clerk's mind anyway. And thus the whole identity verification thing was irrelevant, he was just suggesting a practical solution to the customer's problem.
What's sad is that the business owner would probably be willing to sacrifice your business for the perceived benefit that he/she is getting from Facebook's WiFi.