If a person gets hurts on the job, and the supervisor blurts out during a staff meeting for the employee to go to the ER..?

I don't understand the problem. How is it a violation of your privacy for your supervisor to tell you to go the emergency room if you were injured on the job? What difference does it make if there was a staff meeting in progress? Whether you were injured right in front of him during the meeting, or whether he only learned of your injury from someone else at the meeting, it was appropriate for him to insist that you go to the ER.

You were mistaken in your comment that it was "nobody's business what happened." Workplace injuries are not only the business of the entire management, but of the various state and federal agencies that regulate the company for which you work.

No, a HIPPA violation would be the doctor actually providing the information to the supervisor.

supes have to write reports on severity and type of injury