There are many things people can do to take advantage of BRG. I've seen people photoshop their screen shots, edit emails, etc to try to 'prove' lower rates. The only way for Hilton to really verify is to get one of their own to confirm and match, as trusting an external resource can quickly add up to a lot of writeoffs. I do think it's bad policy to provide a best rate guarantee and not be able to match special promotions that may come and go within a span of hours or minutes, but I would not go as far as to say this is fraudulent by any means. BRG is something that is overpromised and underdelivered by it's nature.
If it were me running the show at Hilton, and I wanted to implement BRG, I would allow guests to book the room at the lowest rate through any agency that provides it and refund the existing reservation.