Michigan's chances of winning that game weren't very good regardless of who was coaching. Their starting QB is a guy who got ran out of Iowa, they have no talent on that team. Circumstances matter too, if we played Utah to open up our season on the road chances are we'd be starting off 0-1 too, just saying. They played a pretty good team away rather than a cupcake at home like 90% of schools are doing.
That said, I agree Michigan being his alma mater made it an easier sell, but it's not the be all end all. He turned them down once before also. Plus I don't think Michi has ever said we had a realistic shot at Harbaugh IIRC. His stance was always that we should at a minimum make him say no and considering he's one of the best coaches in the game college or pro, that's not even remotely unreasonable. Worst case scenario he tells you no which you're expecting anyway. Best case scenario he shocks everyone and says yes.