I have a car and I have insurance, but if somebody else is offering me primary liability for free, I'll be more than happy to take it and leave my insurance company out of it for small matters.

AARP still gets you liability at Avis and National and Budget. More than a few times when the rates have been close I've used the AARP code instead of the AAA one for the liability and damage cap.

At Avis:

In the event of damage to a rental vehicle when travelling in the United States, as an AARP member you're protected with special contract provisions available through the AARP Program: **

Avis provides primary liability up to $25,000 per person, to a maximum of $50,000 per accident, plus $10,000 for property damages.

Your liability for damage to a rental vehicle is limited to a maximum of $5,000 if you decline to purchase the Loss Damage Waiver (LDW). Note: Review your personal auto insurance policy and/or your credit card benefits to determine if your coverage extends to the operation of a rental vehicle. If it does not, or you do not have personal auto insurance, LDW coverage can be purchased from Avis at the time of rental.

and I believe Budget and National. Those rates are dropping, a few years ago you got 100/300/50 thousand coverage.