True, as a general rule you can't claim both breach of contract and unjust enrichment (or, in legalese, "quasi contract"). And the reason is straightforward: the two theories are, at the core, mutually exclusive, because unjust enrichment is predicated on the notion that there was no contract.  
There is an important exception to that rule, however: if "there is a bona fide dispute as to the existence of a contract . . . a plaintiff may proceed upon a theory of quasi contract as well as contract."
As a practical matter, there are many, many cases that fall squarely into the ambit of this exception - i.e., where the parties vigorously dispute whether in fact they had ever entered into an enforceable contract. Consequently, lawyers often include causes of action in their complaints asserting both theories, breach of contract as well as unjust enrichment in order to hedge their bets, and thereby try to protect their clients' interests - whether the court ultimately finds that there was - or was not - an enforceable agreement.