That is generally true for a CFI giving instruction to others in his aircraft for hire. And I did ask about that, and yes that is more problematic. But I could also get a checkout in an aircraft that I purchase.
According to my insurance broker, many aircraft insurance companies (it definitely varies by company and type aircraft insured) have what's called an "Open Pilot Clause" (or warranty) that covers a pilot not specifically named on the policy if that pilot meets the minimum experience requirements named in the policy and has the owner's (insured) permission to fly his aircraft. Global Aerospace, the underwriter that my broker has found is one of the only underwriters with reasonable rates for Van's aircraft, has such a clause. But they also stipulate the minimum experience for an instructor (CFI) to be used for their required Van's RV checkout, even if not in the insured aircraft, which happens to be the same as their open pilot clause.
It is: Currently effective pilot certificate issued by the FAA, airplane category, with a single engine land rating, who has a minimum of 500 total logged flying hours, including at least 100 hours in aircraft having conventional landing gear, of which not less than 25 hours shall have been in a Van?s conventional gear aircraft.