Just got an email from the BRG folks.
"I apologize for the late reply. Please be advise that hotel weren’t able to adjust your stay as a free night. In order for us to honor the Best Price Guarantee, we will reimburse you with your stay. Someone from Guest Relations Department will contact you for the reimbursement process."
This is a Penthouse night, with a price tag of 2,200 EUR.
Since I have this in writing, I am gonna go along with it.
In addition, as I will be paying the hotel for this night, I expect all the royal treatment that comes with.