See, most medical professionals follow a VERY strict code of ethics. Releasing confidential information is listed among the worst of these just behind "do no harm".
Releasing confidential information ends a career in the profession (worst case), at best really hurts your job prospects in the future.
This is one of those things where you need to live in the medical community culture to fully understand. I use to work in it, I can tell you this, people have been fired for this before. In this case, she was obviously tricked but I imagine still written up for doing this over the phone.
I one time applied for a job after working in a hospital, HR would neither confirm nor deny my working there. That is the level of seriousness this is.