It's illegal to release top secret documents to the NYT as well. It doesn't stop the info from being published, does it? Any third rate private investigator could get your medical records today, if he tried to. If you don't believe that hospitals leak info like a sieve, you're mistaken. And that doesn't even touch the usual Senatorial Staff sources available.
I have seen people lose their jobs over what you are suggesting. Anyone releasing medical info unauthorized are fired on the spot.
If I'm at work and I want to see whether or not a patient has had any other recent blood work done that I can add tests to the hospital can tell that I was in there looking.
We are not even allowed to access our own records without permission.
We were also one of the hospitals that had the victims of teh Amish school shooting. Nothing was leaked.