Yes, but the problem is that what is a "matter of national security" in practice is whatever the government says it is. So this exception is enough to effectively eviscerate the freedom of the press.
Nobody got in trouble in the U.S. for reporting on/distributing the Snowden leaks. There weren't any newspaper raids. Nobody was asked to "keep quiet". Anyone who did censor did so out of mutual interest.
Press freedoms have not been eviscerated here. It's a trendy narrative, but in reality you have enormous freedom to distribute content which was illegally obtained as per the Pentagon Papers cases and others. The worst thing we have here is cozy relationships between the media and the government, but alternative news sources are available everywhere and Americans are relying on them more than ever.
Just to be clear, NSLs are largely unregulated by the judiciary and are frequently overbroad in the information they demand, but they aren't arbitrary gag orders.
They can keep you silent about the fact that you got an NSL (and that therefore there's an investigation going on), but not about the content itself.
Press freedoms and freedom of speech haven't been eviscerated in the US, true, but neither is the US the bastion of freedom of speech or press that it's promoted as. It's reasonably free, and has some weird corner cases like Westboro Baptist Church's activities, but it's not head-and-shoulders above its contemporaries.
Reporters Without Borders puts the US at 46th position in their Press Freedom Index. An awful lot of things can be turned into "national security" issues.
I'm getting 46 from this page, in the graph and in the text http://rsf.org/index2014/en-index2014.php - where are you seeing 32? I vaguely recall it being around 30 last year.
Those aren't great examples -- it's pretty rare to get taken down for simply reporting on IP issues. You can get taken down for distributing someone else's copyrighted content, but I have yet to see the government go after someone for simple journalism. The closest we've gotten to that was the Dajaz1 domain name seizure, but that was because they served up actual copyrighted songs (though arguably with authorization), not because of their reporting.
That said, there's been plenty of DMCA abuse and unwarranted legal nastygrams against journalists, but as far as I'm aware, in every case where people actually took the case to court rather than just giving in, they've won. Our IP system provides for plenty of opportunities for "extortion by lawyer", but it's a different problem than "press freedom" IMHO.
The "hot news" doctrine is mostly dead these days.[1] And at worst, it delays wide-spread dissemination of news for a day, rather than suppress it outright.
From the linked article: "The United States rejected this doctrine in the 1991 United States Supreme Court case Feist Publications v. Rural Telephone Service"
