If you are looking for points from the stay itself (5x points per dollar for stays + any status modifier like 30% for Glob, promo points like 3k per 3 nights, etc) as the WOH Concierge seems to think, then yeah, you don't get points until it is completed. If you are looking for, as I read your post and in my opinion, common sense reads, points from the CC spend (the 1x base earning + 4x on Hyatt spend from the Hyatt spend on a Hyatt Visa for example) by having the stay immediately charged as per the terms of the booking, then yes, they should charge you immediately because that is what the rate calls for. Now, in REALITY, in my experience over 90% of hotels don't actually charge you until you get there even on an AP rate, but they basically reserve the right to and if you cancel before the stay, then they charge you.

I have, several times, needed or wanted the stay charged in advance on AP or even non AP rates, and always been able to contact the hotel and request they charge me immediately. Multiple reasons including accounting, business, credit card offers, etc. Whoever told you at the hotel they "can't charge you" on an AP rate is just 100% flat out incorrect. Tell them you want to cancel the reservation then and see how fast they figure out how to charge you. Just contact them again and politely request that they charge the amount of the stay as per the terms of the rate type you booked because you booked it for that reason. Last time I booked an AP and needed it charged immediately, my concierge contacted the hotel for me and had them do it immediately with zero issues, although 99% of the time I just contact the hotels myself. Had an amex offer recently on a non AP stay and called the hotel and they immediately charged the card in the reservation. Quality service with no issues.