One more day of experience to report:

Yesterday I was seated and given the regular menu. I didn't mention status at that time, but did give my room number. A minute or two later a different very friendly and smiley server came over and said, "Oh Mr. Srodr, we have this special diamond complimenary menu for you to order from!" I said something like, thanks but no, I'd seen that menu the day prior and didn't really like anything on it, so I would be sticking with the main menu.

She walked away with a bit of a defeated look on her face, so it makes me wonder what exactly is in it for them in 'fooling' their diamond guests into getting jipped with that lame little diamond menu? As one of the best Hyatt properties, it seems a strange place to encounter this kind of thing.