In the fine print for the rate "Cancellation policy
Cxl 5 days prior to Arrival"

However, this does start to sound like misleading advertising. Fully Flexible in the travel industry tends to imply that something is refundable/fully able to be changed.

The explanation is almost laughable. I would be pushing this further up the Hilton tree if you don't get an adequate response as well as perhaps through your consumer type bureau.