In general, any school that wants to avoid having their lawsuit against the NCAA dismissed will have to make a compelling case in the filing that:
- They've been harmed by actions taken by the NCAA
- The court is required to address this harm and is able to do so
- The harm was caused by NCAA actions that either:
- Violate the law
- Or, represent a severe breach of the by-laws and were the result of severe negligence or malice on the part of the NCAA
It's the third part that makes it very difficult for a school to sue. Simply being injured by NCAA actions isn't enough. If the NCAA punishes you according to by-laws you've agreed to, then the court's perspective is that you can simply leave the organization if you're unhappy.
Outside of Oklahoma and Georgia, schools typically haven't sued for a couple of reasons, this being the primary one. What's typically happened when a school has been unhappy, is that it is former coaches and athletes that have attempted to sue and the school has very quietly supported them in the background.
You also need to be clear on what "success" means. The courts ruled in favor of the Board of Regents, so that's clearly a success. The Supreme Court ruled against Tarkanian. However, in the big picture, Tarkanian was also successful. He tied his case up in the courts for 12 years and got the NCAA to the point where they essentially gave up due to the cost and effort. So he never had his penalties applied.
UNC's hope would be for the Tarkanian scenario to play out. They will not win the case on its merits. If their intent is truly to sue, then they'll want to focus primarily on making sure the case isn't dismissed, and then focus on dragging it out as long as possible in the hopes that the NCAA eventually decides to settle to get it over with.