FHR rate only asking the room bill must be paid by AMEX Platinum or Centurion card, and in most of cases, the reservation(s) under FHR rate is process by AMEX Plat/Cent REP via GDS system.
In my experience, the FHR rate + frequent guest program's benefits all work as well. I never got a call from my clients to complain about two programs can not combine together. (maybe I am lucky)
FHR benefits included:
-upgrade to next room type (subject to hotel availability and contract room type)
-free continental breakfast up for two per room
-GTD late check-out to 4pm
-some special amenity, like free lunch/dinner for two, or spa treatment..depends on hotel offered