For all the major hotel groups (Hyatt, Hilton, Marriott, etc), all issues that involve hotel stays are resolved by the hotel. No one working in the Guest Service areas of Corporate or Central Reservations will have access to an individual hotel's property management system (PMS).

The PMS is where hotels will attach notes regarding an incident (if there was one). Although, some hotels might also use a separate system to keep track of daily issues (power out during severe weather, fender-bender in the parking lot) that might affect guests.

As such, coleslaw is correct that sending complaints/compliments to hotels for follow-up is quite normal.