No Egbeard, what I am saying is the insurance requirements are more of a factor than your license. So to answer you directly I'm saying it is impossible not just unlikely. Every club or FBO from which I've rented you had to be covered by their insurance, period, full stop!
As an example, the club I currently rent through has a C-182, Arrow and a S35 Bonanza. Whether your license is private, commercial, or ATP before you can rent either THE INSURANCE REQUIRES a minimum of 10 hours in constant speed retract airplanes and 5 hours in an Arrow or S35 Bonanza. So since I already have 20 hours in an Arrow I'm covered. When I decide to checkout in the Bonanza, I will need to get 5 hours in the S35 OR ask if the insurance company will accept my other several thousand hours in singles and twins that are constant speed retracts. My guess is the insurance company will accept my experience, but I am prepared to fly the 5 hours if they do not.
This club also has specific minimum experience as dictated by the insurance company to rent their C-182. Their rule is simple, if any pilot, regardless of license and ratings, does not meet the requirements dictated by the insurance company you cannot even schedule the airplane unless you are accompanied by a properly signed off club instructor.
I don't see how to explain it any more clearly.
Be legal, safe, and smart...