Product: Debt collection

I received a letter from Grant Mercantile Agency ( GMA ) regarding an hospital bill plus interest. When I reached out to the company to dispute it, they acknowledged that there was an error that wasn't my fault and agreed to waive half of the interest. However, since the issue wasn't my fault, I asked them to waive the entire interest and they refused. The history is as follows. 
I was treated by XXXX XXXX XXXX XXXX XXXX. When I first checked in, I filled out my forms, handed them my license, and provided my insurance card. Instead of pulling my address from the forms I filled out, they pulled my address from my drivers license. I had moved and the address on my drivers license was incorrect. I received a letter from GMA stating that my account was delinquent and they were collecting for the hospital. I reached out to the billing department at the hospital and that's how I learned that they had entered the wrong address. The hospital said they would recall the debt from GMA and send me a new bill. Once they did, I paid it in full. They also said there might be another bill from the other side of the hospital that was also sent into collections for the same reason. I asked them to take care of that as well. The person I spoke with said she would reach out to the other billing department and do the legwork for me. Two months later, I received another letter from GMA stating that my account was, once again, delinquent. I reached out to XXXX XXXX XXXX XXXX XXXX and they said they have no record of me being delinquent. They suggested I contact their sister hospital -- XXXX XXXX -- because there are frequent mix ups between billing departments with those two hospitals. I was treated in both hospitals so it was a possibility this was the case. I reached out to XXXX XXXX 's billing department and they also had no record of me being delinquent. I reached out to GMA and they said they would not provide me with the info of who sent me to collections. They suggested I contact XXXX XXXX XXXX XXXX XXXX. I informed them I did. I explained the situation and asked them to remove the interest from the debt. I told them that if I had an outstanding bill -- because it was sent to the wrong address by the hospital -- I would gladly pay it. However, I shouldn't have to pay the interest. They said they don't waive interest. I asked for a supervisor and argued my case with her. She said they would waive half of it. While nice of them, I feel I shouldn't have to pay for any of the interest. I am not at fault for this. When I asked them why they would waive half and not the whole amount, they said they don't waive interest. She told me that the bill was ultimately my responsibility. I agreed and said I was never trying to dispute it. I was never sent a bill because it was being sent to the wrong address. She said I should have known how much I owed and followed up if I didn't receive a bill. How could I follow up on something I know nothing about? After I've been treated by a doctor, my insurance company will send me an explanation of benefits and state that " this is not a bill. '' After that, it can take months until a bill arrives. If it's a XXXX, it can take up to a year before all the bills have been sent out. If I don't have a time frame for when ( or if ) I'll see a bill, I will have no reason to reach out to ask about it.