Nebraska was the AP champion and Texas was the coaches', but I believe the latter was done before the bowls as we beat Texas handily in the Cotton Bowl that year. I believe that was the year Richard Nixon went to the Texas-Arkansas game at the end of the season and declared the Horns champions when they won.
Ohio State claims the title from something called the National Football Foundation.
Thanks, I didn't look in detail. Based on my +/- spreadsheet