There is also an important difference: media piracy can have a somewhat negative image in the eyes of the public, but pirating scientific papers does not. If academic publishers attract too much attention with a lawsuit, and more people understand their revenue model, I doubt that the public would be on their side. So maybe this encourages them to be more cautious.
In fact, Sci-Hub is not a real threat to academic publishers as long as universities do not cancel their subscriptions because of it. Of course, many universities probably won't want to tell their researchers to just use Sci-Hub (because of legal concerns, and because it could disappear the next day). So leaving Sci-Hub mostly alone may well be a deliberate decision from academic publishers.
In fact, Sci-Hub is not a real threat to academic publishers as long as universities do not cancel their subscriptions because of it. Of course, many universities probably won't want to tell their researchers to just use Sci-Hub (because of legal concerns, and because it could disappear the next day). So leaving Sci-Hub mostly alone may well be a deliberate decision from academic publishers.