Wrong. Liability and Damage are on the driver and are required to be carried by the driver whether or not the car is insured. The insurance on the car is only for damage to the car. They just assiociate it with the car for convenience. For example, if you rent a car and get in an accident and do NOT take the rip-off supplemental insurance, your auto insurance is on the line for damage to property and people (but not the car itself).
Look it up somewhere, or ask a lawyer. I know whereof I speak. Insurance is carried on the car. There is usually a clause about covering the owner of the car if he is driving someone else's car, but that is primarily to cover an uninsured car.
When any of my kids got a license, there was no insurance requirement for them, but the insurance on my cars went up. If a kid is the primary driver of a vehicle the rates are astronomical, but the insurance is still on the car.
From the California DMV web site:
"Vehicle owners are required to submit evidence of liability insurance to the Department of Motor Vehicles (DMV) when renewing the registration of a motor vehicle. Trailers, off-highway vehicles, and vessels are excluded from this requirement. Acceptable paper evidence of current liability insurance is an insurance identification card issued to vehicle owners by insurance companies."