If I go to AMEX to book a regular hotel reservation as a travel agent- not as a FHR reservation - whether with Marriott, Hilton, Hyatt, Fairmont/L'Accor, Four Seasons etc - I should get full points and elite tier benefits with the hotel (chain)?

To put it another way, are the AMEX travel agents considered to be regular travel agent, by all hotel chains?

Or AMEX agents considered online travel agents, by the hotels? if the answer to the first question is yes and the answer to this question is no - then why do some hotel (chains) consider AMEX FHR program to be equivalent to a booking by an online travel agency, but direct bookings by AMEX travel agency to be travel agent bookings?