Your analysis of PHI and HIPAA is missing a critical component, and the story is unclear on this point, but if the school is providing health benefits to the staff, then they are absolutely bound by the HIPAA regulations, as employer sponsored health plans are covered by the HIPAA regs.
You are correct that the plans are covered, but I find it hard to believe that the school administration would be plan administrators, with access to PHI. In this instance, the information was provided voluntarily outside the continuum of care. I don't believe it's even remotely connected to HIPAA. But it's a huge EEOC issue.
In essence, a school nurse who gains knowledge of PHI through the course of her responsibilities as a caregiver is bound by HIPAA. So is the benefits rep or plan administrator who is aware of the plan of care. The principal and other faculty would not be bound by HIPAA, although they could be subject to its regs if they illegally broached systems containing that data. The correct response from the teacher would have been: "With all due respect, the date of conception is none of your business". She'll get a nice chunk of change from the EEOC though.