There's are several; legal issues to unpack with respect to this situation. Since Schiano's employment contract apparently has a term that exceeds one year, it is probably subject to the State of Tennessee's "statute of frauds," which is a law that requires certain kinds of contracts (including contracts that are for a period in excess of one year) to be in writing and signed "by the party to be charged" in order to be enforceable. The party to be charged is the authorized signatory for UT. Query whether that must be the Chancellor, or whether it could be the Athletic Director alone. In any case, verbal assurances or commitments would probably be unenforceable due to the statute of frauds.
Schiano would presumably assert, at minimum, legal claims for breach of contract (his employment contract), and defamation of character. The latter claim would not depend on the existence of an enforceable contract. The statement that Currie came out with, about having done considerable due diligence and finding no issues whatsoever with Schiano's character or background, was clearly intended to rebut any inference that UT defamed Schiano. But they still did not hire him, and arguably did so because of his history at PSU. That may present some difficult issues of proof for Schiano.