I used to be an insurance adjuster for a top notch insurance company and here is what we told our insureds.
If you have comp and collision on your personal vehicle you do not have to get the extra coverage when you rent a car. HOWEVER, should you have an accident, you will have to pay for the administrative fees (I've seen them charge $125 and maybe even loss of use for the rental vehicle while it's being fixed) So you will still be out of pocket for your deductible, the admin fee and if the rental vehicle is out of commision for a while the lost revenue.
USAA covers your rental car providing you have coverage on your existing car however, there can be some special circumstances so you need to confirm it with them first. Some credit cards will cover the admin fees and loss of use if you rent the car using that credit card. It's usually the gold or platinum cards. Check your credit cards for this coverage.
If you have an accident, you can certainly be charged a surcharge if you were at fault.