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WORST DAY OF 2016 (details inside and advice needed)

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You bought insurance for a reason. Use it. You will not be precluded from claiming accelerated depreciation/diminished value, nor will you be admitting fault. You are simply putting it through your own insurance who will then subrogate. This is very common. If someone accidentally burned your house down, would you refuse your own insurance and deal with the tortfeaser's insurer on the rebuilt? I sure wouldn't.

Tell your insurer you will not accept any finding except 100% liability on the other driver given the circumstances of the accident but you understand they need time to do their due diligence. I'd tell Gallagher Bassett that you're an honest person and you do not claim for neck/back injuries when there are none and expect for him to treat you in the same manner and not play any games. Tell him you have a lawyer in the family even if you don't (white lies are allowed to ensure you're treated properly) that you won't hesitate to call if liability is not accepted and all costs are not paid. Don't mention accelerated depreciation/diminished value until after your physical damage claim has been completed. Do not sign a release or waiver.
 
Look at it this way - you walked away - your car is a tank and will be fixed for ~$8K. You can't fix things if you aren't around to collect the insurance monies. This poor guy never had a chance.

semi-vs-car.jpg
 
Guys thanks again for all the advice and suggestions. Just want to leave an update for references.
I ended up using my own collision to get it fixed since I really didn't want to wait for the other party, not even knowing for sure that the result would be in my favor. I paid my deductible and will be waiting for Geico to deal with the other party.
The damages include the rear left quarter panel, the rear bumper (and the sensors on it) and the shield below the bumper. Everything included, the repair cost was about ~$13k and took 3 weeks most of which went to the rear panel replacement. Got my car back recently and it looks good as new.
If any of you is interested in details of the repair, let me know here or send me a PM.