I think that as many answers and categories as Jeopardy runs through in a season, and as many seasons as the show has been on, it was pretty much inevitable that the show would have an LDS category sooner or later. I doubt the LDS PR department had anything to do with it.
Does anyone remember the Mormon Monopoly board game that came out years ago. I'd love to have it now. I think Boardwalk and Park Place were Nauvoo and Palmyra or something.
Seems like the one I'm thinking about was more professional looking. You got "get out of spirit prison free" cards and the chance cards were so lame. I've thought it would be a hoot to play with a bunch of exmos and some great margaritas.