They've done beat KState once. Rematches are tough.
To your point:
Prior to Conference Championship Games, about the only way for two teams to have a rematch was to play each other in a bowl (after having met int he regular season). The last 8 times that happened, TTBOMK, the team that
lost in the regular season won the bowl game.
Kinda' weird.
But Conference Championship Games have been different.
Of the 29 rematches in Power Five CCGs, the regular season winner won 18.
The most common rematches occur in the PAC 12.
Of the 7 Pac12 rematches, the team that won the regular season game won 6 of 7 in the CCG
Stanford over UCLA
Stanford over Ariz State
Stanford over USC
USC over Stanford
Washington over Utah
Utah over Oregon
The one outlier was Oregon over Arizona (Arizona had won in regular season)
Rematches are a lot rarer in the Big Ten. Only happened three times:
OSU over Wisconsin - OSU won both
Wisconsin over MSU (MSU won in regular season)
Wisconsin over Nebraska (Nebraska had won in regular season)
In the Big 12, there have been 8 rematches - the regular season winner won 5 of them:
Oklahoma over Kansas State
Texas over Colorado
Oklahoma over Missouri
Oklahoma over TCU
Oklahoma over Baylor
The three where the regular season loser won:
Nebraska over Texas (Texas had won in regular season)
Oklahoma over Texas (Texas had won in regular season)
Baylor over Oklahoma State (Oklahoma State had won in regular season)
There have been 6 rematches in the SEC CCG. The winner sweeping 4 times:
Alabama over Florida
Florida over Auburn
LSU over Georgia
Auburn over South Carolina
And 2 where the regular season loser won the CCG:
LSU over Tennessee
Georgia over Auburn
In the ACC CCG, there have been 5 rematches. The regular season winner won twice - the regular season loser won three times:
GaTech over Clemson
Clemson over VaTech
Clemson over Notre Dame (Notre Dame won in regular season)
VaTech over Boston College, twice VT won the CCG after losing to BC in the regular season