HIPAA has a minimum necessary standard of disclosure. Ideally, EMS staff should try to put a stop to lurid interest of that sort (keeping in mind that their first focus will be emergency medical care, not policing who happens to be nearby, possibly for legitimate reasons) and could be held liable if what was leaked was due to things they actually said to a third party.

But I think you would probably have to pass a test of reasonableness. If you are getting medical treatment in a public space, there's only so much EMS can do to protect your privacy.

In practice, it's really hard to strictly comply with HIPAA and many institutions routinely violate it in small ways.

From what I gather, law enforcement, such as prison guards, have their own rules covering confidentiality. But I don't think a prison guard would be covered by HIPAA. A leak by a prison guard would have to be dealt with via other channels.