The secondary insurance language does not refer to the waiver. It's been a few years so I may not be exactly up-to-date on everything but by law, rental car companies have to make sure you are legal. That's why, the legitimate companies, do not ask your for proof of insurance. So let's say you carry minimum coverage in Alabama and get in wreck in Florida which has higher requirements. The rental car company will cover the difference between your Alabama policy and the Florida minimums. The insurance that they typically want to sell you is the "damage waiver" which isn't really insurance it's just them waiving their ability to hold you responsible for damage to the vehicle unless you violate the terms (e.g. You're drunk, you tow something, etc...). The benefit is that there is no deductible and it doesn't go against your own policy. The cons are that it is extremely expensive and still only covers the car. If you need liability then you'll need to buy the liability portion.
Since you have already verified through your insurer that your policy covers rental cars then the decision is entirely up to you and what you want to do. The one exception is when people travel with friends and they want their friends to drive the car. People get in a lot of trouble doing this when they don't buy insurance through the rental company. Let's say you & I go on a trip together and you rent the car but I'm driving and get in an accident. Typically what happens is that your insurance company says they have no idea who I am and are not going to cover it. My insurance company will say that my name isn't on the rental agreement (even if I'm an additional driver) and therefore I'm not responsible for the damage. You are then up the creek.