Here is my recollection of relevant events from that period when I was offering some counsel to Ohio's then director of legal affairs who sent me copies of Ohio's trademark registration documents.  (I was then responsible for promoting and protecing for my company's trademarks and brands.)

Ohio regisered OHIO as a trademark for use on licensed apparel and merchandise.  (Other universities in other states had done likewise.  Examples, as I recall, then included Indiana, Michigan and Florida.) 

When an entity registers a trademark, another entity has a stipulated period during which it can file a protest. 

If the Trademark office finds the protest has merit, the protestor can bring a suit that will be heard not in a Court of Law but in an Administrative Court.

There is no obligation for an entity that has registered a trademark to notify any other entity that it thinks might want to protest.

That having been said, just before the protest period would have ended regarding Ohio's registration of OHIO, someone from Ohio did in fact unwisely disclose to OSU the registration in question.

OSU rushed to file a protest before the deadline for doing so.

That's when the media began having fun with the issue.  The Wall Street Journal, for example, gave it tongue-in-cheek treatment on the front page of one of its sections.  Matt Lauer on Today did a balanced treatment of the dispute - and ended it with hoisting an OHIO logo'd coffee mug.

Then Bob Glidden and OSU's then president got together and agreed on a settlement - which was virtually identical to what was covered in Ohio's registration.

To the best of my recollection - which certainly can be flawed - no formal suit was filed.