The SEC has also played conference games against nonconference opponents. Their scheduling back in the day was "creative" at times. Georgia Tech would not play the Mississippi teams at all, even in Atlanta. Of course, this was in the day of bowl games, teams wanted to position themselves for a gaudy bowl shot.
If a program was struggling, you could play your 6 conference games and win 3, and then 4 pastries and win 4, and be 7-3 and probably get a bowl invite if you had a good fan base. If your team that year caught a break or three and was pretty good, you could end up 9-1 at times and get an Orange Bowl invite.
You would never play any Big Ten teams of course in a bowl game, nor a Pac Ten team. It was ACC or Big 8.
There was one year, I think 1971, when UGA has a so so team and an invite to the Sun Bowl. Nebraska was in the running for an NC and somehow lost their last game and all the major bowls were committed, they lost out going to the Cotton who invited whoever beat them. So, the Huskers dropped all the way to the Sun Bowl. They apparently were not happy and demolished UGA. Dooley said he realized after that that they needed a real strength program at UGA.