Hotels collection – different card charged than handed to receptionist

Hello, I have a question regarding the Hotel collection bookings and which card is charged when “Paying at the hotel”.

Having added a cashback offer for a hotel chain to one of my Amex cards, I looked to book said hotel and saw it was also offered with the Hotel collection benefits (if booked via Amex travel via my Plat card benefits – not the card that has the cashback deal).

I read said offer terms and unless I misunderstood it seems to state that the final bill “must be settled with an Amex card in the name of the booking cardholder”. The way I interpret this is that if I book with my Plat card, I can settle with any card under my name. – Is that wrong?

Either way, I chose “Pay at hotel” when booking and at the hotel asked multiple times at check-in if I can pay with my Offer Card, to which they repeatedly said yes. I indeed inserted the Offer Card into the terminal for pre-auth, saw the amount, entered my pin, etc. They said it’s all fine and that the inserted card would be charged at checkout.
I was happy that this way I might also receive said cashback deal.

Ultimately, on the day of checkout, I received an app notification of the charge that looked correct (meaning that it would apply to the card I inserted). I even received another smaller charge for a snack also for the same card. However, neither showed up as pending when checked.

Few days later, I see that both transactions now appear under my Plat card statement and non cashback deal was triggered.

I totally get that I was trying to combine offers and don’t mind having lost one, or totally accept if I’m labelled an idiot for trying this. I am merely just super confused as to how this happened and if anyone knows how this works. The staff at the hotel were a bit incompetent (they e.g. gave us the wrong room) so I wouldn’t be surprised if they did something wrong, but I would like to know if I did something wrong.

Thanks a lot!