It is possible the guy was trying to injure himself so as to avoid a jail cell or something. It would be hard to prove. If he was otherwise restrained, they should have strapped him in. Normally people do not wear restraints in larger vehicles like buses and large vans. But I would think if the person had their hands and/or feet restrained that they should also be strapped to the seat. If not the current practice it is high time that start doing it.
The only thing I can draw from is movies and TV shows. Usually the people have handcuffs and leg chains but no seatbelt. But that is proof of nothing in the real world.
I have had first hand accounts of these joy rides in the patty wagon from guys in the 70s. Broken bones, etc...
Violent starts and stops, sharp turns, they were trying to hang on with their teeth.