You might find this interesting. Penn State was undefeated. So was Ohio State. At the time it looked like Ohio State was going to win out and they were already ranked number 1 overall. Nobody thought they would lose a game.
Bowl games used to secure their teams in November, before all of the regular season games were finished. Paterno left it up to his team to choose the bowl game. They could choose from the cotton bowl vs Texas or the Orange Bowl. Miami was the favored destination over Dallas. None of them felt they had a shot at the National title because at the time, Ohio State was a Juggernaut. Michigan upset Ohio State to end the season.