car insurance for dependent...

Hi. This may be more of a legal question... Financial advice I've
gotten
says that I should do all I can to separate my teenager's ownership,
payments, insurance and any other records of a car from me. This
is because any insurance company paying a claim because of anything
my child does, will try to recoup from whoever has any money and is
associated in any way with my child's driving.
My current insurer wants to fight this perception, citing two (only!)
cases where a parent was still successfully sued. I suspect he just
wants the new business. He want us to associate our child with a
junky car to lower the premium, but the coverage will apply to any
of our cars, and to increase our umbrella coverage to cover the
new risk...
Opinions sought.
thanks
Joe