The BRG terms require you to pay the Hyatt Daily Rate for a base room (or higher category for resorts). BRG rates are not the Hyatt Daily Rate, they are a discount rate. You are still treated as a normal paying guest (the same as if you are on any other full, corporate, or discount rate). None of that affects the requirement for suite upgrades via points to pay the listed Hyatt Daily Rate.

[Yes, I know that when you have a successful BRG, the rate type is listed as Hyatt Daily Rate. But that's not an argument that you are actually paying the HDR. You're still paying a discounted rate and thus not entitled to use a points upgrade.]