Heard from someone that works with a diff insurance that if a Father let's his son drive and is not on the policy then they will refuse to cover.
IINM ,In NY state the insurance companies are required to pay for anyone in the household that's why the insurance companies add your kids automatically so they can rate the policy correctly. They have to pay out, they may choose to non renew you if this happens.
I know of a case where a son was not on his father's insurance and was driving his friends car and got in an accident, the victim came after the fathers insurance bc the son lived at home. In the end the fathers insurance didn't pay out bc the father owned a 2 family house and proved that his son lived in the other apt.