If you find a room in the Fine Hotels & Resorts program and then you find the same hotel room for a lower price on the same date through a different source, you can get a refund of the difference.  However, the price only applies to publicly available rates and excludes things like package rates, corporate discounts, loyalty program discounts, and rates provided by opaque booking sites (where you don’t see all the info until after you commit to your booking). Additionally, you have to submit your claim to American Express before you check in for your stay.