That didn't happen, but it then took plenty of political influence in the mid-1990s to ensure Baylor being the only private school included when half of the Texas schools from the SWC merged with the Big Eight to form the Big 12 Conference, leaving TCU behind.
Now the small private Christian schools, with only about 90 miles of Interstate 35 between their Texas campuses, are competing for more than a share of the Big 12 title. TCU and Baylor have identical 10-1 records and are in the mix for a spot in the new four-team national playoff.
''I don't think anybody that's involved cares one hoot and holler about how they got there,'' said Teaff, executive director of the American Football Coaches Association the past 20 years, equaling his time as Baylor's coach. ''The important thing is that they're there.''
Baylor's place in a major conference was in jeopardy again at the start of this decade during a much more widespread outbreak of realignment. The Big 12 survived despite the departures of four schools and was restructured as a 10-team league that included the 2012 entry of once-shunned TCU.
Baylor senior offensive tackle Spencer Drango laughed when asked this week if growing up he ever imagined seeing Baylor and TCU as national contenders.
''It was always if Texas wasn't in the running there was something wrong,'' said Drango, from Cedar Park High in the Austin area. ''It was like a sign of the apocalypse if Texas wasn't in the running.''
Now the Longhorns are losing to the Bears and Horned Frogs.
Baylor clinched its first Big 12 title last season with a 30-7 win over Texas in the regular-season finale. TCU is coming off a 48-10 Thanksgiving night romp that pushed the Frogs up two spots to third in this week's College Football Playoff rankings, three spots ahead of the Bears.
When left out of the original Big 12 lineup, TCU went to the WAC, then Conference USA and the Mountain West, winning or sharing titles in each of those leagues and going to 13 bowls from 1996-2011. During that same 16-season span, Baylor was 60-126 overall with a record 29-game Big 12 losing streak and only two bowls.
The Frogs were set to go to the Big East before Big 12 changes let them stay closer to home. Now they only have to beat Iowa State, the only team without a league win, to get a piece of another conference trophy.
''It just proves what people said a long time ago when we went to 85 scholarships, that parity was going to hit college football,'' said 14th-year TCU coach Gary Patterson. ''Baylor and TCU both have good football teams, they both have good football staffs, and they both have passionate fan bases, simple as that.''
Teaff said both universities have made a total commitment to their athletic programs in recent years, with ''imperative'' support from the respective boards and administrations. He said they also made ''great hires'' in coaches Art Briles and Patterson.
Briles is the fifth Bears coach since Teaff left in 1992. Baylor has consecutive 10-win seasons for the first time in school history.
''Baylor never won a Big 12 championship until last year so making history is good, but it's about winning football games now,'' said Briles, in his seventh season. ''We're winning games and trying to create consistency in a program and trying to prove that we belong with the nation's elite in college football.''
Baylor is home Saturday night against Big 12 co-leader Kansas State to close out the first season in its new $266 million stadium on the edge of campus and the banks of the Brazos River. The Bears have won 24 of their last 25 games in Waco the past four seasons, the lone loss being to TCU in their first Big 12 meeting two years ago.
The Frogs also end the regular season at home, wrapping up their third season since a completed $164 million rebuild of Amon G. Carter Stadium in Fort Worth.
Fourth-year Bears defensive coordinator Phil Bennett held that same position at TCU in 1997. In between those jobs, he had a six-season stint as SMU's head coach (2002-07), when the Bears were perennial last-place finishers.
''They're both unbelievable places,'' Bennett said. ''I can remember vividly when Baylor couldn't win a conference game, and that's why I put them on the schedule when I was at SMU.''
Times have certainly changed.