Never, heard of a car rental place ever asking for more than your credit card. The do NOT need to know my business if I am traveling full time in my RV nor have I ever heard that question being asked.
That's why I find it so easy to just pay for a po box at the "UPS Store".
No ID act to jump thru to get one and the po box number is on the same line with the address as a Suite #. (in fact it has to appear on that same line or it won't get delivered)
This works as an address for EVERYTHING you need without having to claim a domicile or drive all the way to SD! :C