Yes, they will owe you $x and you will still owe the hospital $x - but that's often not very useful, as they don't have any money (and you do). You may desire

Yes, they will owe you $x and you will still owe the hospital $x - but that's often not very useful, as they don't have any money (and you do). You may desire to transfer the debt onto them, but the hospital will absolutely not accept that. Why would they? If a bank owed you $1 million, and they said "oh, now Jim owes you that money, not us" you would similarly refuse.