It is an insurable interest - a leased car will be neither owned or registered to the user but the user can still insure it because his insurable interest is that he is, for want of a better expression, renting the vehicle.
Yes, flip-flop, but you cannot insure a hire car against, say, theft, and expect to be paid out in the evnt of it being stolen. The hire company may insist that you pay for any such insurance, but you will be simply indemnifying them against their potential losses, not your own.