a few months ago i was driving my old vt down a dirt road in the middle of outback wa when i hit a couple of roos, the car wasnt too bad but i ended up leaving it on the side of the road because the radiator was damaged. when i rang the insurance company and explained the situation they decided to write the car off and within a week they had paid out the money (they did deduct the excess however).. all without seeing the car.
they didnt even bother towing the car, they just left it on the side of the road until a few weeks later when the police and the shire responsible for the road contacted me and told me to get rid of it.
check your insurance certificate of currency to make sure youre covered for $5000 agreed value, it sounds like they are really trying to screw you over. If you didnt have to worry about the other persons car I would have said you should tell the insurance company to stick the claim and their policy and fix the car yourself but at least youre getting all your stuff out of it before they get their hands on it
good luck