Ohio State football is way, way more about state pride than Michigan is. Ohio State gave an identity to the disenfranchised coal miners and farmers of Ohio back in the day and it's been passed on for generations. You've guessed correctly, it's not about the school. But I'm not seeing the problem with that... if anything, I wish Michigan football was such a major uniting force in the state.
"The University of Illinois is also in turmoil. The university sports an Interim Chancellor, an Interim Athletic Director, and an Interim Football Coach; the game will be played at Soldier Field, making this an Illini Interim Home Game."