The official answer from Hilton was that each property sets their own rules, and the Hilton Mystic no longer rents rooms for Saturday only stays. I know they have in the past, as I have stayed there many times just for a Saturday.

This is also the only place I've ever stayed that only gave Golds one breakfast instead of two when there were two people in the room, so they must sit around in an empty room on Saturdays coming up with their silly rules.