The owner get a report with a partial CC number (I believe the last 4 digits), date, time, amount of charge, and amount they are keeping of the charge.
The owner would have to match the partial CC with his copy of the receipt to know who you are. While it can easily be done, I'm sure most owner don't go to the trouble.
I had this happen to me last year. We had a party for about 30 people at a local restaurant, and since they were in iDine, I decided to prepay the amount over several months (since total amount was above the monthly limit). I did it okay for the first month, but when the second month came around, they did mention it to us (I forget exactly how). I guess for parties you weren't supposed to be able to get the discount.
Since the discount was for the max amount, it would have required a $600+ bill, which they probably don't see too many of. I likely wasn't that difficult for them to track it back to us. For more regular purchases though, I don't think the restaurant would go thru the effort.
Jeff