When you called the first time, did you point out that you didn't stay there and that you didn't earn the points? If you did and the hotel still didn't do anything, AFAIC, you have fulfilled your obligation. If they only told you that they looked up "your" number but you didn't tell them that it wasn't actually you, you owe them a chance to sort it out.
No. In fact, if it were a bank, I'd insist that they do it. Money errors can be a nightmare to sort out.
Mike
Mike