I'm not getting this at all. I have frequently stayed at Hiltons and Marriotts where someone else is footing the bill, and have never had an issue with my loyalty program number being entered in the record, with receiving any elite benefits I may be entitled to, and receiving a copy of the folio at the end of the stay for my records, even if the bill is addressed to someone else.
The incorrect assumption is that OP was entitled to any elite benefits. As has been pointed out, many bookings are not. The issue isn't who is "footing the bill" but how and the rate issued. That my great aunt Ida paid for the room is not the same situation.