I believe the hotel is correct. Book and pay is the key.
I learned this the hard way once, kind of. Under SPG I booked multiple rooms. They gave me benefits but when I checked out, my sister paid so I was denied nights and points
My sister didn't care about nights or points. Was 5 villas/ suites at high season for me so meaningful points and nights for plat
I llearned then everyrhibg is book, stay and pay