It's in collections? Send them a letter saying you don't owe it. Show proof you paid it, proof you tried to resolve it, and ask them to stop collections and correct your credit. They likely will.
If not, you just need to talk to the right person/department at the hospital. This runaround is typical. Just keep calling and trying to talk to a relationship manager or someone who handles more than just billing. They call them different things, but you want to get to whatever that person is for that institution. The billing department won't help you. Escalate, keep calling, annoy them if you have to, they are hoping you'll go away, well make them put in the extra effort to get you to stop calling. Talk to different departments until you get to the right person.