Anyone know what Amex's policy is on their car rental insurance when redeeming a free day award?

I believe technically you may not be covered and so should choose the rental agency's LDW coverage, correct?

But here's a potential wrinkle -- at my local Hertz I don't have to hand in my free day rental certificate until I return the car. I presume, if something were to happen to the car, I could have Hertz just charge the rental to my Amex (Platinum) and tell them I changed my mind about using the certificate. In that case, I should be covered by the Amex insurance, correct?

In a related question, is Amex coverage in effect if I use a discount coupon/promotion code for, say $15 off a rental?