I could be wrong but I was under the impression that most of the major insurers (at least in the US) cover you if you're authorized to drive the vehicle, even if the vehicle isn't on the policy. Of course, YMMV and you should check your own policy before declining Turo's insurance.

That said, good to know that Chase won't cover Turo rentals. I should check the CDW coverage at some point on my Diners Club MC (which is also primary) to see if it's the same.