Auto Insurance Claims: What if insurance companies estimates disagree?, settlement issues, independent party

Question
I was in an auto accident with the other driver at fault.  I contacted my insurance company while still on the scene to be sure I got all the information I needed from the other driver.  My company started a claim, had me get an estimate, and determined the car was a total loss, and gave me a figure they would pay.  They told me I had the option to take that payment, a lesser payment and keep the car as salvage, or to have the other driver's insurance make an offer.  They say I would be paid the amount the car is worth minus my deductible, and would get the deductible back when the other insurance company pays off.  But now the other company has contacted me and seems to be just starting their claims process, in fact they want me to have one of their adjusters look at the vehicle.  So I am wondering, what if the other company were to determine the car was not a total loss, and I had accepted my company's offer?  Should my company have made that offer when the other company had not agreed to the amount (or even that their driver was at fault) yet?  I specifically asked if there were anything I would need to do to get my deductible back and was told no, it would all be taken care of.  But I can't see how that could be the case without agreement by the other company.

Answer
No need to worry.  You can settle with either company.  If you settle with your company, they will subrogate against the other insurer to recover what they paid plus your deductible.  In very rare cases, the companies disagree about repair or settlement issues.  If this is the case, your company would file arbitration and an independent party would decide who was correct.  But as I said, this is very rare and not likely.  It would be impractical for the companies to agree on everything before setttling claims.  You should just settle with whomever you prefer, keeping in mind you'll probably have to wait several months to get your deductible back if you choose your company.