Ohio State did, in fact, participate in a bowl game in 2012.
We know that it happened based on our analysis of available historical records, such as eyewitness testimony, video images, and anguished letters (illegible in their drunken scrawling though they may be) addressed from Jacksonville, Florida to Columbus, Ohio.
From what we can gather, the 6-6 Ohio State Buckeyes played the 6-6 Florida Gators in a college football bowl game on the 2nd of January, 2012. The details are fuzzy, but two things are certain: Ohio State lost that game, and it was one of the dumbest, most useless games of football ever played.