Oklahoma was indeed Big XII football champions, as was K-State. Not co-champions, just champions.
K-State was indeed Big XII basketball champions, as was KU. Not co-champions, just champions.
Spin it however you want, in whatever way you want, with whatever reasoning you want. The Big XII rules say there is no co-champions, only champions. If the record is tied at the end of the season, there are two champions. The trophy says Champion, not co-champion. End of story, thank you, goodnight.
(all in fun by the way, yet totally serious about it)