the reason it hardly changes. is because it hardly changes the payout you'd recieve. youll get what your given. ive never heard anyone 'haggle' the offer upwards once a claims made. so just dont undervalue and your good to go
I wrote a car off a few years ago, my fault, fully comp so OK. I rejected their first 2 offers, and they asked for supporting evidence to justify my valuation of the car. I found adverts for the same type of car, in similar condition with similar mileage, history etc. I found 5 adverts all above the best offer they had made. I submitted these, and they increased their final offer. The insurance company are trying to negotiate the claim, and like any negotiations, they will low ball you first. Same as any offer to settle a claim, whether it be for an insurance claim, compensation claim etc etc, never accept the first offer, justify your claim and ask for more.