That's still not entirely true.  A suburban hit my 81 2wd toy in the bed, spun me and hit again in the cab and door.  Insurance deemed it a total loss, cost of repairs exceeding the value of the vehicle, then cut me a check.  I retained the clean title in my name, swapped out the door and continued driving it with a clean title. 

Where it would have changed is if I had full coverage insurance and only my insurer was involved.  The options then are usually get a check for full value and give them the vehicle, or recieve a partial payment and keep the vehicle, at which point you can go through the salvaging process or use it for parts.  That's how I got my first f4i, the guy solo crashed it and bought it back, then sold it to me and I went through the salvaging process.