I have been through this scenario twice. Both were the fault of the other driver, both were said to be totaled. Neither of them received branded title status. Neither were valued over $10,000. We received a generous check in each case and were allowed to keep the vehicle in both cases at a very low cost.
How's your neck? Make sure to rub it constantly while you talk with their adjuster.

1952 5-window - return to "as built" condition | 1950 3100 with a 235 and a T-5 transmission