Was at Hyatt Crystal City a few years ago and was bitten by a bug in bed. Had a big booboo on my foot. Took a taxi to the nearest hospital, they took care of me. Came back told the hotel, they were very understanding, wanted me to keep hush hush. I did!
They passed me to their insurance company which took care of medical bill and treated me fairly.

They key here may be how you as from them and your GP status. If they see you travel a lot and an incident like this has not been taken place earlier, they are more open to taking care of you.

Hope this helps!