I have never been required to show proof of any insurance at AVIS, NATIONAL, HERTZ, U-HAUL, or PENSKE in any state (including many, many rentals in CA.

There is no requirement in CA that I carry a card proving insurance when I drive a rental car. And I don't carry one. And the big rental companies never hassle me for it.

There is, however, a requirement that I carry a proof of insurance card in my owned vehicles in CA. And they are in the glove box.