Maybe I've just been lucky with the properties I have stayed at, but I've only been faced with two scenarios:

1. Either I am asked for my name and room number prior to seating and I never get a bill at the end - just walk up and leave (mostly resort style properties and when breakfast is served in lounges)

or

2. I am given a bill (at restaurant or room service) and fill it out 100% as if I were paying at any other restaurant. Example:

Subtotal: $50.00

Gratuity (20%): $10.00

Total: $60.00

Ive never been charged for just the gratuity portion. Given how varied Hyatt properties are with handling things, I am sure that sometimes the server is only getting my tip and other times they are getting my tip + 15-20% for the diamond comp.

Now, plenty of times I have been charged for the breakfast in full by mistake, however I just take this up with the property at checkout or with Hyatt online (I never call) and usually within 48 hours I am refunded the entire amount.