Ok, so now you have to determine if the insurance overpaid to the hospital simply due to they paid more than their contract called for or if they paid money that you should have paid (out of pocket, co-pays, deductibles) If the latter, you owe the insurance company if they have not received a refund from the hospital. If the hospital has refunded the errant payment, then you owe the hospital.

If the overpayment was simply that the hospital was paid too much but your out of pocket expenses would not change, then the insurance company needs to seek the overpayment from the hospital.
Without reading all the germane paperwork, it is difficult to guess exactly what you are dealing with. I would keep at the hospital and the insurance company until you receive an explanation that really does explain what happened.