Then BYU has to be ranked #11 or higher (some times much higher).

So while BYU may not be competing against THAT conference champ they may be competing against other teams (and even other conference champs) to get a higher ranking so they even qualify for an at-large bid.

It is a nuance that you just are not willing to admit exists. BYU is competing against everyone to get their highest ranking possible so that they can qualify. And the lower ranked any auto-bid is then the harder they have to compete to get a higher rank...

They are not competing with a specific conference champ for that conferences auto bid. But they are competing against them for a higher ranking for the possibility of being ranked high enough to be an at-large.

In reality - those teams are not competing with BYU for their auto bid and BYU is not competing with them for their auto bid. In fact those teams are not competing with BYU for the at-large bid per se either (assuming they get their auto bid and don't have to fall back on an at-large selection) but BYU certainly is competing with every other team for the highest ranking possible to qualify for an at-large.