It's not complex at all. The risk is all on you.
Good way to look at it. I was thinking of CAP which has self-insurance (Corporate) on some flights with lots of liability (all) on not just the PIC, but the entire crew, and then completely different scenarios when flying at the direction of the Air Force under a live mission.
The chart for the three different mission classifications and insurance is mind-blowing.
In addition, most "renters" policies specifically exempt CAP flying and many aren't aware of that. AOPA's underwriter makes adding a CAP rider policy a simple checkbox, that many don't notice and don't pay for.
Considering these are generally new Cessnas worth a lot more than the average rental Cessna "beaters", many pilots don't even think about the additional liability, nor things like what happens if the worst happens with a Cadet aboard doing an Orientation flight.
A couple of pilots did over $20K in damage to a T182T here in the not too distant past during a proficiency flight, and the left seater and the CFI split a $5000 bill. And they probably got off easy.
Flying "other people's airplanes" when not a named-insured on your own policy that covers your very specific flying, can be a very expensive game of Russian roulette if you have any assets at all.
Often "owner" policies really aren't covering your backside either, if you've set up a typical LLC ownership arrangement. It all depends on the wording of the policy. Any wording that you're covered in "rental" aircraft is if the LLC rented the aircraft, not the pilots of the LLC. A very deep "gotcha" that can bite "owners". The LLC has the insurance, not the individual.
It's a jungle out there!