I do not own my car, and thus do not have auto insurance of my own (otherwise, auto insurance typically follows you where you go, including to any rental cars). When I went to rent a car, I was told that I was required by the State of Georgia to have my own liability insurance, and that since I did not have my own auto insurance, I would have to purchase the rental company's supplemental liability insurance (SLP). Is this true? Wouldn't the rental car company already have coverage for the state-mandated minimum liability insurance?
This liability insurance issue depends on every country. As for the US in particular, every state may have a different policy. It is indeed required in many states to have liability insurance. In most states where liability insurance is required, the rental car company will provide a minimum coverage. But be careful, as stated in Hertz policy:
Financial Responsibility Limits by State
The following chart lists the Automobile Financial Responsibility Limits of the various states. Hertz is not required to provide such minimum protection in all states. However, the purchase of LIS will include primary protection which combines these minimum limits of protection with an excess insurance policy to provide the first $1,000,000 of combined bodily injury and/or property damage for each occurrence.
Georgia : 25/50/25 (Per Person Bodily Injury/All Persons Bodily Injury/All Property Damage (in thousands of dollars))
Hertz clearly says the liability is not always provided. They add:
At many Hertz locations, you receive secondary liability protection, and, in a few locations, no liability protection under the terms of the Rental Agreement from claims of injury by others against you resulting from an accident with your rental car. Some locations provide primary protection under the Rental Agreement. However, in those situations where protection is provided by Hertz, such protection is generally no more than the minimum limits required by individual state law. (See chart for these Financial Responsibility Limits.)
So, clearly, it depends on every rental location. Avis, in its FAQ (Protections/Coverages>Automobile liability ...) is clearer on which states are concerned: there is no provided coverage for California, Texas and Utah. In Missouri, the state's minimum coverage is provided if the customer has no coverage on its own.
From the name (SLP) of the suggested liability insurance option, it is possible your rental company is Enterprise. Even if not clear, the words they use suggest they do NOT provide any liability insurance at all without SLP:
If the renter accepts SLP, Enterprise provides third party liability protection up to the applicable minimum financial responsibility limit.
the renter should examine his or her personal insurance policies or other sources of coverage that may duplicate the coverage provided by SLP.
So I would recommend you to read the fine prints of your rental car company to figure what its policy is exactly regarding Georgia, to know if you need to suscribe a liability insurance option or not.