The BRG exists for a reason and it is to help SPG weed out lower rates than they offer, and punish the hotel for allowing that. I would think after your first few BRG claims that the hotel would ensure the lower rate gap is closed, unless they don't care about the penalty they receive for each approved BRG claim.

I thought there was also something in the T&C about only 1 BRG claim allowed within any specific metropolitan area over a certain time period? I vaguely recall such a restriction, but am not entirely sure.