Certainly. Every employee has a duty of loyalty to the employer implied in his or her contract. A betrayal of that loyalty is potentially a breach of contract.
A simple analogy will make the point. If the assistant in the butcher's shop told a customer that the meat on sale was of poor quality and overpriced, the butcher would have every reason to dispense with that assistant's services. The teacher in this instance was equally guilty of disloyalty and deserves a warning that such conduct is unacceptable.
This should not be confused with the protection accorded to "whistle-blowers".
Where employees have serious concerns, they should have the right to make representations to the appropriate authorities, without fear of reprisal.