You may have not read the offer, but that doesn’t make it shady. The Amazon/Amex deals are nothing new and being sold by Amazon has always been a condition.
When a discount is being applied, Amazon will make it very obvious when calculating the total. Near the totals and tax, you will see a line item for the Amex Promo that reflects the discount amount. If you don’t see it, you’re not getting a discount. You’re always agreeing to be charged the amount shown when you click the Place Order button.