All states (AFAIK) require all cars to be insured at least to state minimums. Therefore, all rental agencies carry a state minimum liability policy on their fleet (as well as umbrella policies for higher limits).

Where the question exists is whether this insurance carries over to renters or is only for fleet usage (employees driving).

Every company's rental agreement will specify that the company does not, where allowed by law, provide third-party insurance. Most states do not require third party liability insurance to be extended to customers (NY and NJ are two exceptions; there may be others), so no, you would not technically be covered by the rental agency's fleet policy.

That said, I am sure people get around this all the time. Every rental car should go out with a certificate of insurance in the glove box. While not intended for customer use, I would not be surprised if customers find this slip and provide the name of this insurance company to the third party. The third party may very well file a claim with that insurance company, and I would not be surprised if that insurance company didn't ever bother to go back and communicate with the rental agency to verify coverage.

So, technically, no, you are responsible for providing liability coverage unless you purchase the rental agency's liability policy. In practice, however, things may be different. Not that I'm encouraging anything!