The section below is copied from a standard auto policy we sell which shows that most insurance policies state under the liability coverage sections that:;

-Insurance agreement Part 1 liability to Others
(a) If you pay the premium for this coverage, we will pay damages for bodily injury and property damage for which an insured person becomes legally responsible because of an accident.
We will also pay for property damage to a rental vehicle or loaner vehicle caused by an accident that occurs while such vehicle is being used by you, a relative, or any other person with the permission o you or a relative. (NOTE: if you purchased this coverage under your policy, (Liability, Collision and Comprehensive ) you may not need to purchase additional coverage from a rental company.)
Damages include prejudgment interest awarded against an insured person. We will settle or defend, at our option, any claim for damages covered by this Part1 section.

The only reasons to purchase supplemental car rental insurance is for the following reason:
-Some Auto insurers will vary on this coverage leaving you naked if a claim arises
-If you only carry Liability the Collision and Comprehensive coverage will be excluded if you damage the rental companies vehicle.
-You are still responsible for the loss of use of the rental companies vehicle.

You can see your insurance will cover most cases but for claims reasons and loss of use reasons it might be good to take a look at Auto rental coverage.