Sherman Antitrust Act. Historically SCOTUS has decided that some acts (i.e. price-fixing) is considered illegal per se, other actions (i.e. possession of a monopoly) must be analyzed under the rule of reason and are only considered illegal when their effect is to unreasonably restrain trade. Now how SCOTUS defines "unreasonably restrain trade" will most likely be left up to which previous case(s) is referenced in the majority's opinion.

If SCOTUS references Standard Oil Co. of New Jersey v. United States, then its opinion could be different than if SCOTUS referenced Chicago Board of Trade v. United States or even NCAA v. Board of Regents of the University of Oklahoma. Remember Justice Stevens in the majority of opinion noted that not all restraints of trade were unreasonable. An example of what Justice Stevens is referring to is the national TV contracts for the various pro leagues in the US/North America. Since the TV networks are negotiating directly with the NBA, NHL, NFL, MLB, and MLS instead of the individual teams, the league's contract is technically "restraining" each individual team from entering into its own national TV contract.

As far as how the courts rule, I do think the court of appeals would most likely reverse whatever the district court ruled. If nothing else to kick the can down the road to let SCOTUS establish the precedence. Since the SEC would still have the "freedom" to schedule non-conference games against the AAC, C-USA, MAC, MWC, Sun Belt, and DI-FCS schools, SCOTUS may not see it as a "restraint of trade" because the SEC schools are able to make money from those games. Also, it would not "restrain" the SEC from negotiating future TV contracts because the SEC and its members earns a certain amount of money every year regardless of the opponent. Now don't get me wrong, I do see the argument where it would be a "constraint of trade." I am just not sure it would be as black-and-white as some other antitrust cases.