What an astonishing (lack of) response on the part of the hotel - whether or not the door completely latched, what brought the intruder to her particular door?? Something drew him there - unless they have people who walk in off the street who check for unlocked doors every night, which I kinda think the hotel ought to notice, eventually. He might've been from another room down the hall, or an employee.
I haven't been to that particular hotel, but most I travel to have security cameras on every floor, public area, and, I suspect, on the elevators. I can only assume these cameras are recording.
First off, call the police, and ask if there have been other reports at this property, second, demand to see the security tapes. And 20 minutes to respond to an intruder report at 4:00 am?? Guess everyone was sleeping ...