Thank you for the informative responses. Obviously, the CDW is not the issue here because the card covers that. It is personal accident and third party liability.

So do you folks have any recommendations for what insurance I can get for a rental? Does Amex have a product? Annual insurance does not make sense for me as I don't have a car and only rent occasionally (twice or thrice a year).

As a student, I don't really have assets that I need to protect (maybe 20k max).