I dont think they allow BRG on SLH.
First thing I checked when I saw the price difference.
"The following brands participate in the Hyatt.com Best Rate Guarantee: Park Hyatt®, Miraval®, Grand Hyatt®, Hyatt Regency®, Hyatt®, Andaz®, Hyatt Centric®, The Unbound Collection by Hyatt®, Hyatt Place®, Hyatt House®, Hyatt Ziva™, Hyatt Zilara™, and Thompson Hotels® "