Some years ago I was driving into Hartlepool along the A689. Just before getting to Hartlepol I pulled out to overtake a car towing a trailer that didn't have any lights. Just as I'd moved into the outside lane the other car, no indicators, pulled out in front of me, there was nothing in the inside lane, hadn't a clue why he did that. He then swerved across the inside lane and into a bus stop, I was well distanced from him, I thought he was parking and started to drive past him in the outside lane putting the inside lane between us. Just as I almost got level with him he swerved 90 degrees and drove straight across both lanes to drive over the central reservation. There was no gap in the reservation, not even a foot crossing. I went into the side of him, broadside.
The first person on the scene as it happened was an off duty copper. He gave me his name as a witness. I submitted my claim. Eventually my insurance company sent me a letter telling me that the other party had claimed it was my fault, he said that the accident had taken place about 200 yards nearer the town and I'd gone into the back of him at a roundabout. He had a witness, his next door neighbour.
I contacted my witness and explained the situation. He said that he hadn't actually seen what had happened so he wouldn't get involved. I protested that he was there and saw the positions of the cars and the other bloke was at right angles to the road with his front wheels on the reservation. He just said he couldn't make any inference from that and refused to help.
My insurance company said they were going to treat it as knock for knock. I told them I wasn't happy.
I then got another letter from my insurance. They said he'd got another witness, this time on the other side of the road and a lot nearer the roundabout. It was the same name and the same address. I called my insurance company. They said they'd never seen anything like it, but they were still going to settle knock for knock, I told them again I wasn't happy, and that it was obvious fraud. They said they were going to settle and if I didn't like it I'd have to take the hit myself and go to court at my own risk.
What I found out was as long as there's nobody injured the cost of a minor car repair is far better than having the expense and hassle of a court case. It all boils down to the money.
My message after all this is that you might need to take the hit, metaphorically this time, if it's just a matter (to the insurers) of a few quid to fix your car. However it's encouraging for you that at least in your case they're telling you to proceed. I hope you have better luck than I did.