I'm curious though what Hyatt is doing about these drained cards, particularly the ones bought directly through them.
It's pretty easy to know when & where the card was used at. You can call customer service and get that information yourself. Then all they have to do is trace the card back to the hotel folio and determine who used them. Not sure what they could do at the point but they would have the name of the thief and could file charges or something.