The number of conference games means something. But not as much as you are claiming.
Alabama played 3 conference games against teams with losing records. Vandy, Arkansas, and TN. They ended the season with records of 5-7, 4-8, and 4-8 respectively.
Ohio State played 5 conference games against teams with losing records. Indiana, Rutgers, Maryland, Nebraska, and Illinois. Those teams ended the season with records of 5-7, 4-8, 4-8, 4-8, and 2-10, respectively.
So you will excuse me if I don't act too impressed over their scheduling an extra 4-8 team and a 2-10 team.
In fact, Ohio State played 6 teams that ended up with a losing record. Alabama only played 4 teams with losing records.