In an accident, advice dealing with other ins company

Never let "their" insurance call the shots. You have an insurance company and they work for you. Make sure you get them involved and make them do the work. At the end of the day, your company is the one that insures the car and has a vested interest in it's condition and the satisfaction of you...their customer.

The other guy's insurance company is only looking out for their bottom line and their customer...which isn't you.