Insurance & a moral duty of care
As pointed out above there is no duty on the part of the aircraft rental agengy to have anything other than third party insurance cover on the aircraft, this seems to be reflected in the flying order book for all to read.
The question I would be asking of anyone who rented me an aircraft on this basis what else is missing from the plot ?
In theses days when legal action almost always follows an accident to rent an aircraft to someone who you suspect has not got the appropriate insurance cover is in my opinion morally wrong. No doubt it is OK in the eyes of the law as it clearly stated in the flying order book but such a policy would leave me wondering if I would want to trade with people who engage in such sharp practices.