While this is with Chase's LHR and not Amex. I remember reading a travel blog where a guy was staying at the Nomad in Las Vegas. Same type of thing happened, he was supposed to get $100 F&B credit. His confirmation & everything showed this. At the front desk through they said they will only honor $50 instead of $100. He noted that the front desk told him they aren't responsible for 3rd party bookings. Thankfully Chase reimbursed him for the error. But, it does appear at least that the hotels do have the power to honor or not honor the bookings. It'd be nice if amex would back you up & reimburse you though!