clause? It's a ranking based clause. It doesn't matter who the teams are, what conference they are in, or anything. It could be 4 SEC teams as the at larges or it could be 4 independents. The other teams refers to anyone that doesn't qualify as "displaced conference champions and the highest‐ranked champion from a non‐contract conference".
As far as BYU goes, BYU does get paid by the CFP. We are part of the contract, albeit at an insultingly low level. But beggars can't be choosers.