My wife took my Sonoma in after an accident for the adjuster to look at the minor damage. It was still driveable. It was the third time I was hit driving home from work due to the mess made of IH-45 when they were putting in the NASA RD-1 bypass. They told her it was a total and they would take the truck. She told them in no uncertain terms that she would be in big trouble with me if she came home without the truck. Total just meant they wouldn't pay for any damage above 75% of the value left on that beat-up truck. We kept it, still insured by them, but didn't have any more damages to claim after that.
Did any of the airbags go off?
Also, the rules for what an insurance company can do with a car that they treat as totalled vary from state to state. We had an old Crown Vic that got clipped by someone trying to pass on the left on a double-yellow. The damage was easy enough to pull out, and didn't even require repainting or touchup. When it came to the insurance, they gave us the totalled value, less some amount for us to "buy" it back from them, and thereafter we only had accident coverage with them. This was in New York.
I don't know all the details of what transpired with my relative, but it was my understanding that the amount of money the insurance company was offering simply wasn't enough to put the car back in useable condition - with the airbags replaced - so my relative chose to take the totalled amount and left the car with the insurance company.
To be quite honest, I would think that some enterprising auto insurance company would add a separate rider for airbag replacement that, for an additional premium, would take that factor out of the equation for determining whether the car was a write-off or not.