Not really.
Privacy Rule
The Privacy Rule took effect on April 14, 2003, with a one-year extension for certain “small plans”. The HIPAA Privacy Rule regulates the use and disclosure of certain information held by “covered entities” (generally, health care clearinghouses, employer sponsored health plans, health insurers, and medical service providers that engage in certain transactions.)[10]
Note that there is no provision for the Sponsor of the Plan.
With that, if she signed a morality clause in her contract, they had a right to fire her. If she cannot prove monetary damages from the passing of the information she volunteered, she doesn’t have a leg to stand on. Without the HIPPA law to fall back on, she has to prove slander. The truth is not slander.
It was tactless and she should have not answered the question. If I were her employer, I wouldn’t have asked that loaded question.
As others have rightfully indicated, we are discussing 2 entirely separate issues.
The firing for breach of contract, the school was within its rights to do so, agreed, tactless but legal.
On the use of the teacher’s PHI, the quote you provided specifically mentions employer sponsored health plans. Now, this is all theoretical, as the story does not make clear whether the employer is the sponsor of the health plan. I have been operating under the assumption that the school is the sponsor, but that is only an assumption on my part.