Careful casting those stones. OSU has 'Dayton YMCA' in the record books as well. https://en.m.wikipedia.org/wiki/1892_Ohio_State_Buckeyes_football_team
And three games in one season vs. Ohio Medical. https://en.m.wikipedia.org/wiki/1896_Ohio_State_Buckeyes_football_team
TTUN was also playing Harvard and Yale (national championship teams in those days) during that period. Not saying they don't have a HS team in the books (I've found one), but they also played a lot more out of state competition than the Buckeyes did prior to the Western Conference being formed. OSU mainly played teams like Kenyon, Oberlin, Case, etc.
Counting wins prior to Theodore Roosevelt cleaning up college football is just bad statistics. It's not even the same sport.