My understanding is that renters insurance in the USA covers the renter for damage to the aircraft, if the insurance company tries to recover the cost from them. The aircraft insurance is for the benefit of the owner. The insurance company will pay the owner, but retain the right to try to recover the cost from other parties at fault i.e. the pilot.
I haven't heard of a similar thing in Australia, but have always wondered whether I was being naive or whether insurance companies are nicer in Australia and don't chase the renter.