That would be the best path IMO. If they end up not affording coverage it's note due to your actions or even those of the other insurance company, you just had bad luck and got hit by a shitty dude that didn't have his things in order. If that is the case I would go to your own insurance company and see about filing with your collision coverage. If you have that coverage you will have to pay a deductible (usually $500 is the standard) but all the repairs over that deductible amount will be covered by your company. There is even a chance you could have a coverage known as Uninsured Motorist Property Damage or UMPD which would allow you to get your car fixed for free without a deductible if the other company ends up not affording coverage to their driver. However, UMPD is not standard and the majority of people don't carry that coverage, I couldn't tell you if you do or not