I have never heard of a hospital that could hold a patient hostage until the bill was paid!!! I think I would file a complaint with the state agency that licences your hospitals. If you are on Medicare I would file a complaint with them too.
I had turned up to collect her and was told I needed to go down to the cashier to get a release. When I got back to the ward, DW was still waiting in a wheel chair with the nurse on the ward. After I told her why it had taken so long she was pretty ticked at me for haggling over payment as she was ready to get back home.
This was 1990, less than 3 years after we moved here from England, so I didn't really know what was normal for the USA. I certainly don't recall having to pay on release when I had my back surgery earlier that year in a different hospital. It is very strange looking back on that Saturday morning arguing with the cashier in the hospital to release my wife.