Booked a best flexible rate. Found lower same room, on Priceline.

Claim was denied saying that the "advance purchase" rate was cheaper on the IHG website.

HUH? This is specifically (and I mean specifically) not how to compare rooms. It says so word for word in the terms:

Matching Terms. All terms of the comparison room reservation, including, but not limited to pre-payment, deposit, number of guests, or other requirements must be equal in all respects to the terms found on an IHG website for your claim to be valid. For example, when you book a room that may be cancelled without penalty on an IHG website, you may not compare it to a room with a pre-paid or non-refundable price on a non-IHG website. At all IHG hotels globally, pre-paid rates on non-IHG sites will be compared with the IHG hotel's lowest available rate on IHG websites. The Guarantee is not available for bookings on websites where the booking details are unknown until after purchase. Sites that do not reveal the hotel brand name until after the payment has been completed (including bidding sites) do not qualify for this Guarantee.