I believe GD came to MSU twice when I was there, and neither time was for a big game.
In 2004 they came to a matchup between MSU-ND when both teams were 1-2 and unranked. They were supposed to go to LSU, but that was a Katrina game, so on short notice they just picked the host of the ESPN Primetime game, which was that. I'm guessing that was simply where they already had enough infrastructure in place to move there on short notice.
Then in 2005, they came to the final game of the season for 5-5 MSU vs. #5 PSU, to see JoePa win a Big Ten title I guess? There were 2 games between ranked teams that weekend. I guess they didn't want to go to Auburn for the Iron Bowl, because they were just at Alabama the prior week. But why not Ann Arbor, for UM-OSU? NOt only had they not been to Michigan yet that year, they didn't go to Michigan at all in 2004 either