I doubt they'd go very far in prosecuting doctors for telling their patients. They would likely want to avoid drawing too much media attention.
A lot of large companies have a far reach in their financial interests, and the media, news organizations, TV stations, and such, all have sponsors.
So no matter what happens, most in the media are not going to report on things that are detrimental to their own income / survival.
You don‘t bite the hand that feeds you, would be the best way to put it, that’s why most stories like this don’t get much attention outside of the internet.
And that’s not even getting into the fact that the majority of all media, (in America), is controlled by just six companies.
And so long as something that’s news worthy, (but also harmful to a sponsor or parent company), stays below a certain level of exposure.
Then all media outlets that stand to lose money, will gladly let such stories fade into obscurity, and are far more likely to spend their time reporting on something like a celebrity wedding, or some other crap.
Because for some reason, anything with celebrities, increases ratings, increased rating means that they can charge more for ad space, which means they make more money.
Because that's what it's all about, money, …even the gag order it's self is about money, (protecting intellectual property, and trade secrets), so that companies with billions can make billions more, unhindered.
So in short, I don't think that the companies that cause news worthy problems would care, since they essentially own the media in one way or another.
And if they can prosecute someone for violating the gag order, they will, even if to do nothing more than to set an example to others who might do the same.
Large companies are known for having arrogant business practices, they know they can do whatever they want, and they know that the majority of the excessively ignorant populace will simply let them.