That is the really bad part of the IHG BRG - having to book the lowest rate when that is often non-refundable/non-cancellable.
The Ts + Cs are a bit ambiguous but if the competing rate includes breakfast then you can book the lowest rate on IHG that also includes breakfast even if it is not the absolute lowest rate available. Sometimes (as in my claim) the lowest rate with b/f on IHG was Best Flexible Rate with Breakfast. There was no Advance Purchase with Breakfast