That would be a fair statement. Certainly my opinion of a school's program is partially formed by its fan base. To be fair, I've probably run into a disproportionate number of frat boys at Ohio State games. A Wisconsin fan was so obnoxious to us at one NU home game that my wife dropped the F-bomb on him, the only time I've heard her use that word in 32 years of marriage.
You, on the other hand, seem like a reasonable person.
Believe it or not, I'm not the only reasonable OSU fan, but as usual the squeaky wheel makes the most noise (or something like that). It just so happens that there are a lot of wheels on the Buckeye bandwagon, so unfortunately even if the percentage of squeaky ones aren't greater than those in similar programs, the numbers are high.
I'm not any different. Growing up to me the perfect season was beating an undefeated Michigan to play and undefeated USC in the Rosebowl. So inadvertently, my second favorite team became Michigan and third was USC. Then came the 90's and the ridicule from the Michigan fans and the media's love of USC in the 2000's. They then became my two most hated teams, until Florida and Alabama came around.
So it's no different for OSU fans And their feelings for other teams. Which is more of a dislike for a fanbase's minority and media hype.