Don't think my homeowners policy would cover it, and haven't heard of any 3rd party company that offers that type of insurance. That said, I don't think it would be wise for UNV to offer in-house insurance. Sure, they could make a few extra dollars off honest people who pay for the insurance and then return the equipment. But all it would take is one shitbag to pay for the insurance and then falsely report the equipment stolen. Said shitbag now has a thermal for the price of a rental and insurance, and UNV is out a few thousand.
As the renter, if you know that you alone are responsible for it, you will take better care of it.
If you treat it like it's yours, it won't get damaged. If you don't leave it laying around unsecured or unattended, it won't get stolen. No worries. Problem solved.