Most car insurance here in the U.S. is sold in two sections. On is for damage to the car and one is for protection against law suits arising from possible negligence, which is called liability insurance. Everyone is required to have the liability insurance by law (to protect the other driver, essentially), but the collison/comprehensive insurance to repair the car in theevent of an accident is at the discretion of the owner. It is required, however by the lender if the car is financed.
The liability portion is usually the same for certain age groups or other demographic considerations. However the collison/comp insurance is related to the value of the car.
Many policies do cover a rental car but not everything, so one has to be cognizant of what their personal policy does cover. Since the liability portion is actually for the driver not their car it usually covers one for that purpose when renting or eren borrowing anothers car. But the knowledge of what one's policy does cover is their responsibility...