Absolutely false. I had a new Jeep Wrangler get rear-ended (by a Smart Car of all things) with $13k+ in damage, including a bent frame, bent floor tub, and twisted roll cage, all of which was repaired.
So…? The statement to which I responded didn’t make any distinction and is wrong regardless. Unibodies and body-on-frame can both be straightened. The former is more difficult, but doable in many accidents.