Stayed at a property last weekend on an AMEX FHR rate to be paid at the hotel (not prepaid). I received all benefits of the Marriott program and all benefits of the AMEX FHR program. I received points and nights within a couple of days just as if I had booked on Marriott.com

If I had done a prepaid AMEX FHR bill, I would have received 5X AMEX points but perhaps not the Marriott program benefits. Most suggest I wouldn't.

If I booked on hotels.com/expedia/etc., I wouldn't get benefits or points.