It depends on the state an circumstances involved in the accident. Typically, the owner of a vehicle is liable for the actions of anyone that drives that vehicle.
So, the onwer could be liable even though your son insures and drives the vehicle. There are instances where prosecutors or other parties may seek damages from the responsible party only and there are instances where state laws limit responsiblity to the individual involved in the accident.
As the owner of any item, you should make sure that it is properly insured and that all liability is covered, regardless of who has the item under their care, custody and/or control. For example, if you owned a home but your son was living in it and had renter's insurance. You would still be responsible for the home and you could be responsibility for any liability that occurs at that home.