IME Hyatt, Hyatt Regency, and Grand Hyatt have the printed list of what they offer, but this doesn't mean that something else is impossible. I would expect PH and to some extent Andaz to be able to acquire almost anything for you that's legal and maybe some objects and services that aren't.

The last time I was in a HP it was a new one which is larger than most and had more food choices available in the gallery. I noticed a big flat basket on the counter next to the bar cash register that had a collection of toiletry things for sale. I suspect this was similar to the "keep" items on the printed list, but they weren't free. I've never noticed this in other HP locations.