From my memory, and IIRC and FWIW, you need to both reserve the rental with your Amex and pay for some part of the rental with the card - balance after coupons, upgrades, SATNAV, etc.

I signed up for the Cent/Plat service where you are automatically covered upon reservation [U.S., most of Europe, most of Asia, etc.] by the Amex insurance [CDW, theft, and supplemental] for a flat ~$8/day.

I recently redeemed some Hertz vouchers in Europe and Amex said that as long as I used the card to reserve the rental and pay for the taxes and any upgrades that I was covered fully.

I don't know if it’s the best deal going but it is nice to have one less thing to worry about/have to remember.