No way would I trust the desk agent on what the added insurance covers.
OP, if I was that concerned, I would first call my auto insurance company and find out if they sell a "temporary"/"rental car" policy. Maybe not, but never hurts to ask.
Then I would look at 3rd party. Allianz (who does a lot of
trip insurance) offers rental car insurance.
https://www.allianztravelinsurance....WJjhtLHpTVLSDETEyBh-oUpqg3-TzvNcaAvbsEALw_wcB
Also check, as others have mentioned, your credit card to see what, if any, they provide.