We've never needed proof. By waiving their insurance you agree to pay for any damage. And you're liable for your deductible. Just read the info on the places you initial on the rental agreement. They care more about you being able to pay for the damages than anything else. Driving any car, you are the one insured for any liability by your policy. You do have to insure the cars you own, but anyone else's you drive is covered under your policy for liability and the other company will come after yours for payment of damages. Just check your policy and check your coverage for a rental car.
Rental car companies offer insurance, but they cannot, by law, make you buy theirs. Don't let them bully you. I'd only do it if you don't own a car and have no other auto insurance. Once again, (like on extended warranties), the car rental companies make a lot of money on the policies they sell since very few of their cars ever have claims filed against them.
We belong to Hertz Gold and we have to do very little when renting a car. It's waiting for us when we get there.