Also this is as much a lawsuit persued by the state of Ohio as it is Kent State.
The state may have had little to do with it. Since Kent is a state university, they can ask the AG's office to handle basic legal matters for them (contracts, property, etc.). The AG can turn them down if it's outside their expertise (e.g., trademarks, libel/defamation) or if there would be a conflict (e.g., suing another state entity). Also, filing the suit may have required a vote from the trustees.
Also remember that this was in Kent's county, so they likely had a home court advantage.

An appellate court may see things differently.