I have always been under the impression that when you rent a car and you own an existing automobile that your coverage "Extends" to cover the rental..Still I took out insurance when renting. This "extension" also applies to a newly purchased vehicle for a period of days (not for long)
When my wife crashed our "New" (4 days) old used jeep into a tree at 50MPH my insurance company told me: Yes, both Michigan (Where I'm registered) and SC (Where it happend) have rules like that but.. the motor home is NOT AN AUTOMOBILE!!!!
(Says automobile on my policy but what do I know).
So yes, get the insurance.
By the way how much would it have cost the insurance company to cover the accident? About a dollar.. All I wanted them to do was sign and return the Financial Responsibility form..There was never a claim made.