You definitely need liability insurance. As everyone says, it's way cheaper to buy it through your auto insurance policy than to buy it through the rental car company for the rental.
But as for the rental car company requiring it.... nah. They may tell you they require it, but it's actually none of their business. They just really, really want you to buy it from them, because they make a lot of money on it. They do require you to sign a waiver that says yes, you were offered the insurance, but declined it. That's their out if anybody tries to sue them based on the fact that you were driving their car when you caused an accident. The waiver establishes firmly that it's your liability, not theirs, so you better have coverage if you decline theirs.
I've rented a lot of cars down south and each and every time they try to sell me the insurance and I decline it. How hard a fight they put up varies a lot... I've had some agents who accept my firm refusal and say, Just initial this waiver... I've had other agents who tell me various lies, horror stories, tell me that the rental company requires the insurance. I just keep saying "I am covered. I decline the liability insurance."
And then, when they give up and do the paperwork, I check very carefully to make sure they haven't sneaked the coverage onto my bill... that's happened twice. I made them go back and re-do the paperwork. Not sure how it would play out if I were in a hurry on one of these occasions where I hit a hard-sell agent, because it can eat up a lot of time, but so far I've won.