American Express Travel Amex Travel Lowest Price Guarantee scam Internet

I recently made a room reservation via Amex Travel on the phone about 3 weeks out from date of check-in.  The first thing I mentioned to agent was that I remembered seeing Lowest Price Guarantee on the room/hotel I was interested in.  The booking agent said to submit the claim after making the booking and before the cancellation policy applies.  This indicates to me there is some time between making the booking and cancellation kicking in.

I submitted the claim minutes after making the booking.  Amex claims that because the room reservation is not cancellable, they will not honor the lowest price.

Amex should never have offered the Lowest Price Guarantee for this hotel/booking. It is impossible for ANYONE to be able to submit a claim and get a refund on the price difference.  Maybe that is the idea?  I cannot imagine that a company like Amex with a stellar reputation would stoop to a bait-and-switch tactic.
 
If I am offered a booking with a price protection and informed I should submit a claim before any cancellation penalties kick in, it is understood that there is a window of time between making the booking and when the cancellation penalties kick in, allowing me to submit the claim.
 
It is truly shocking they have stooped to this level.