I actually used the Amex program to my advantage a couple of years ago when I bought my last new car. Since the program worked, and maybe still does work a bit like Priceline (a general search for unidentified dealers within a certain distance from the zip code you enter), I went online and searched for all dealers within a 200-mile radius from my home. One dealer in particular had a very low price for the car I wanted, and I figured out from the mileage that it was probably a dealer in the Baltimore-DC area. I then reentered a search, using a Baltimore zip code, and what appeared to be the same dealer went from being 180 miles away to 10 miles away.
Taking a shot on the specific dealer, I didn't enter the program to identify the specific dealer (and bind myself and the dealer to the program) but just went to the dealer in the Baltimore area during a weekend visit with some friends there. When it came to doing the deal, I gave the salesman the sheet I had printed from the Amex site with the price for the car with all of the options I wanted.
I told him, "I don't know if this is your dealership. If it isn't and you can't do the deal, I'll just click on the button on the Amex site when I get home and get in contact with that dealership. But if it is your dealership, then you know I can ask to put at least $5000 of my purchase price on my Amex Plat card (a requirement for a dealer to participate in the program, at least at that time) and I've gotta assume you're also paying Amex some kind of finder's fee. I'll split that amount right now with your dealership; here's my price."
A couple of minutes later, I had the car at my price. Could I have gotten the car for less? Maybe, but the price I paid was probably $5000 less than I would have paid if I had visited a dealer nearer my home. Well worth the money.
I think the car buying program is a great information source, but there's a lot of truth to the idea that you'll save money on the car by using it for that purpose only and by paying by traditional means.