But you need to speak to your insurer too. Also, just because they start the ball rolling doesn't mean they have accepted liability yet.
You may find after weeks of hire cars and repair bills they wiggle, they did with me. That is when my insurer jumped in and I presume sorted it. But with insurance you really need to be 100%.
We retruned an S Class with damage repair and they didn't say anything. It had been pulled and painted and was not perfect. That was a few years ago now.
Their insurance company contacted me to organise repair and car hire so I take it that means they have accepted full liability. Should be getting something in the post today to confirm it all.