He was born in Ohio, went to high school in California and probably did lots of exciting, non-Wolverines-related things before playing college ball in Ann Arbor. His brother-in-law was an assistant basketball coach at Michigan State, too!
So I'm sure there's a perfectly good reason for this picture of Harbaugh wearing a Michigan State hat.
The Majors' Ryan McCumber dug up the image, which shows Harbaugh posing with what appears to be one of his sons. (Jay Harbaugh, is that you?) In any case, here's the head coach of the Michigan football team wearing a Spartans hat.