Oklahoma Farm Bureau Insurance They want me to claim the accident wasn't their fault to settle. Tulsa Oklahoma

On May 15, 2021 I was stopped at a red light (it was about to turn green) and I was slammed into by a lady in a 3 month old Dodge Ram truck. My wife and I both suffered minor injuries, with my wife very sore longer than myself). The young woman profusely apologized and admitted she was looking over at her son with a Slurpee. She admitted fault (although it was obvious as I was at a complete stop with another vehicle in front of me) to both my wife and myself and again to the police and her Insurance agent.

They responded very quickly and issued a check for my car damages. When our medical treatment was done they made an offer to pay the medical bills and give us each $1500 for our injuries. We are not sue happy people and the other driver was so upset at hitting us we had no problem in settling. When the paperwork came it had all the normal wording but specifically denied fault (" I understand and agree that this settlement is the compromise of a doubtful and disputed claim and that the payment is not to be construed as an admission on the part of"  drivers name "or Farm Bureau, by whom liability is expressly denied.".

I could not, in good conscience, sign this knowing it was a lie. I contacted them to have them tell me this is mandatory. I offered to forgo the $3000 for them to remove that clause and put any other language to protect them from further litigation and settle, they refused. After several back and forths I told them I would pay my own medical bills and turn to social media as I do not want to sue anyone. I asked them to send me the bills so I could pay them. They didn't send them or return my calls.

I called them today and they said they were going to pay the medical and if I wanted to pursue the personal injury that I could. They said they could do that without settling the claim which leaves me with the possibility of a rate increase as liability is not established. Am I crazy or is possible for them to protect themselves and still do the right thing without making me go against my morals?

I could easily sue the driver in small claims court and have a ruling that shows the driver was at fault. This would unnecessarily put her name out there even though the insurance company would still pay the settlement.