All insurance companies will try as much as possible to pay as little as possible. Even more so when you have to claim from your own policy. If you have a third party fault then it is slightly different as they have to put you back in the position had you not had the accident and/or cover all your other losses/expenses and inconveniances. Your own policy is not likely to do such.
I've had several non fault accidents and have never claimed thru my on fully comp policy for several cars. My thoughts are that simple, as it's not my fault, I should not have to pay XS or have any of the headache claiming such back. I have always pursued directly through/from the third party insurer and ended up receiving 100% of car value etc and no XS to pay.
This is exactly the reason why I did not claim from my policy when my Omega caught fire earlier this year. I had no body else to blame so couldn't claim from 3rd parties. I decided rather than go through my own insurance and get next to nothing for a 99 S Reg TD Elite with 140k and no history and then have the insurance take their XS too, iti was better to cancel my policy. I got most of my premium back as I was lucky I had only had the policy for about a month and a half. I'v now stripped the car, got out the bits I think I can sell. Had fun taking rest of it apart and then wighed it in.
End result, with the refund and money for weighing in the car, I've at least equalled what I would have been offered by the insurance, not paid any XS and still got parts to sell to make some more money from the car.
I'm only gutted as the car has gone and I wasn't able to keep the engine and gearbox as these were still strong.
Sorry it's a bit late now but just my 10p.