This contract was written stupidly on both sides. The buyout was too high, the clause about any NCAA rule set this mess up. I actually think unless it's a significant violation, KO deserves the money, or at least a significant part of it. I'm not a lawyer, but I'd also think that the fact of an investigation isn't the same thing as having committed a violation, which is another factor in R probable outcome of a negotiated settlement.
The basic rule of contract construction is you read what it says to understand the intent of the parties in their agreement. You don't add what should have been there. Where there is ambiguity, then a judge or arbiter may look outside the four corners of the agreement to ascertain contract language meaning. The argument that Ollie is involved in "minor" infractions is at least on the surface a losing argument.
UConn is entitled to the bargain (their lawyers were smart - it was the perfect proviso because it's hard for KO to object to its inclusion. What's he going to say? "No, I should be permitted break NCAA rules"). KO's not so smart lawyers should have put qualifications on it such as "material violation" or "material violation, which after NCAA investigation, results in any sanction that results in [name bad punishments]".
So KO is down to arguing a few things - anticipatory breach, breach of the implied covenant good faith and fair dealing, and potentially tortious interference with contract depending on what UConn and its "agents" where doing beforehand.
The only argument that really sustains in regards to "it's only minor infractions" is commercial reasonableness which means all contract terms are interpreted in the context of what is generally understood as reasonable and customary under the circumstances. The line of attack that firing for minor infractions is unreasonable and doesn't rise to a level of just cause is on very thin ice, because everybody in college sports knows the NCAA rules are very exacting and particular, and also the NCAA previously sanctioned UConn when KO took over and the school had a heightened interest in ensuring compliance. So, KO is hard pressed to argue immateriality.
With exception of UConn potentially going out talking to new candidates before he was fired, KO is on the losing side of the case. My prediction is they settle for $5 Million with an extended payout period.