Yes... but "renters" hull insurance may not be the same as "owners" hull insurance. The idea behind renters hull coverage would normally be that it covers you if the owner's policy doesn't name you as the "insured." If a renter is declared a "named insured" under the owner's policy rider permitting renting then the renter would normally just be liable for the deductible on the owner's hull policy. The extra cost (if any) of that rider would be built into the rental price.
Think about it this way. If 20 people rent a plane worth $40k and each of them plus the owner gets a 'hull policy' those 21 people might be spending something like $25k a year to insure an asset worth $40k.
The correct scenario is that the owner has a hull policy that allows renting, and the renters purchase insurance against the deductible of that policy plus liability insurance. That means each of the 20 renters is paying perhaps $200 a year for insurance vs. >$1k if they each had hull policies.
I'm not aware of any insurance that provides insurance for the situation described... specifically one rents from an owner that has not properly insured the aircraft and is operating the aircraft in violation of their policy. It appears that may be why the insurance companies are throwing their hands up here. Same idea as if you try to use your personal car as a for-hire taxi with normal insurance and then get in an accident. The insurance companies are just going to see that as their out and will throw their hands up.
Until anything else happens, this is all the owners problem now. Let him sue the renter, but as others have said there is plenty of grounds for a counter suit... especially if the owner misrepresented their dodgy insurance situation with the renter.