The “private” part of that is not enforceable. Though I’d personally love if it was so I could buy a cup of coffee at an airport in 2023 without using an app or credit card.
Or until they cancel the transaction.
If you order the coffee, they say “okay that’ll be $2.87”, and you try to pay with cash, they can cancel the order. Poof, no debt.
Now if they drop the check at your table after you’ve enjoyed the cup of coffee, it’s different IMO.
They'd temporarily moved their debt onto you and now had to accept it back again. But it hasn't gone away.