The Big 12 does not have any stipulation to do that. Now, I think I read only 9 of 84 teams have ever been selected outside of the top 12 teams. But they can choose whoever they want.
here is an excerpt from the Big 12 website. Once the CFP is filled, then the Sugar gets first pick. They could pick anyone as long as they are bowl eligible.
“
Big 12 Bowl Partners
Once the CFP has filled its bowl slots, Big 12 bowl partners will make selections from the remaining Conference teams. Following is the order of selection. A bowl may pick from any available teams with .500 or better records when it reaches its spot in the selection order. After the placement of those teams, slots will be filled from among the pool of remaining teams.
Allstate Sugar
Valero Alamo
Cheez-It
Texas
AutoZone Liberty
Guaranteed Rate
Lockheed Martin Armed Forces Bowl*/SERVPRO First Responders Bowl* “