I had a mate who worked in a proper crash repair place many years back. He told me that as long as the car is repaired properly, that is properly jigged, prepped and welded by someone who knows what they are doing, then the car is just as strong as original. As he said, cars are welded together in the first place. He reckoned that there were loads of cars bought second hand that had been in quite serious shunts.
He did also say that the ones done by bodgers were dangerous though.
The guys in the video certainly look as if they know what they are doing. I'd be more worried about it rusting after the various coatings have been compromised, than the strength after the repair.