Forced Conference Membership/Antitrust Issues

I thought I would raise this for the board because I have not seen it discussed here or elsewhere. But (directing this primarily to other board attorneys), but wouldn't we have a pretty good antitrust argument if the conferences/bowls/etc. ultimately made it impossible for us to compete in major college football without being a member of a conference?

I'm pretty sure that the NCAA could not mandate that we be part of a conference, for reasons similar to why the NCAA cannot restrict television rights of its members schools. But what about the tie-in agreements between the bowls and the conferences? What if the CFB Playoff dictated that you had to be a conference champion to participate? What if the conferences made rules where member schools could only play each other (i.e., no out-of-conference games)?

I keep hearing about the "changing landscape" of college football, but I'm having trouble coming up with a way where we could be forced into conference membership without there being a possible competition issue. Of course, practically speaking, I think that Jack and Co. would rather kowtow to the conference overlords, as opposed to fighting it.