So I didn't have the easy experience everyone else was describing. I went to the Diamond check in and got a trainee. She tried to give me an Executive suite, which is a smaller suite and not what I had booked through Amex Fine Hotels. I had reserved a back up reservation with points and cash and a suite upgrade. When I was certain that the diplomatic suite mistake rate would be honored, I cancelled that one. So finally after several back and forths with the manager, she agreed to give me the diplomatic suite. Then when she gave me the paperwork with the rate, it was the usual rate. GULP. So then I tried in vain to explain showing her the paper with the rate I booked and the difference in the commas and zeros (which is how this happened on Amex's side no doubt). She just didn't get it at all. So I asked to actually see the manager. She was terrific. She explained to the trainee how to "fix" this when I check out. So I am now in the club lounge because after more than a half an hour of negotiations, my suite is not ready.
So, I spent a good bit of time talking to the manager about the experience of having all these people make these mistake reservations. At first the Grand Hyatt had no idea it had even happened. And the first people were charged the full amount and were reimbursed by Amex.
The main takeaway I got though was that it has been tough for the hotel not because of the mistake (they are being reimbursed by Amex) but because of the no shows and people checking in and not checking out. Basically the suites are all tied up and so they cannot upgrade their members and indeed the hotel is full on the books but it isn't.
So, I would say if you are not going to use your room, cancel it. I need to do that myself as I booked one in December I cannot use.