He should have gotten a ticket for not having insurance, not being registered, and for not wearing a seatbelt; he shouldn't be liable for the accident, if it wasn't his fault. If he didn't get cited for the lack of registration and insurance, the cop didn't do his job.
If the kid causes an accident and has no insurance, he's responsible from a civil perspective, but collecting would be a pipe-dream. The innocent party would have to have their insurance pay the claim, then the insurance would have to go after him (unlikely), or just eat the cost (realistic).
In my younger days while living in Hawaii, there were so many "Brahs" and illegals running around the islands without insurance, the state had a "no-fault insurance" standard. If you were in an accident, your insurance paid your damage, and the other person's insurance (if they had any) paid theirs. It made no difference who go cited for the accident. Makes sense for some locales.