The real question...
...is "what constitutes public vs private communication?"
Certainly, my highly visited website about the Beijing Tea Market would be considered public if I posted a "threatening message" there, but what about my family genealogy website? It's equally open to the public, but is visited less, which could open up a slippery slope of determining at what traffic level a "private" website becomes "public".
How about facebook and twitter, where the user can control the visibility of what they write? Surely, if my privacy settings only allow my friends and family to see my comments, then that should be considered private communication, in my opinion, but I'll bet the government would disagree.
If the government can decide what is public vs private arbitrarily, then what's to stop them from deciding that your phone call to your friend down the street is no longer private? What's to stop them from saying that your pillow talk with your spouse is no longer private? Clearly, what I say to my wife in our bed is no business of the government, but at what point does their right to classify our communications as public or private stop?
I hope this case addresses some of these issues, though I'm sure that ultimately it will just result, as it always does, with the little guy bending over as we slowly erode our freedoms.
Of course, there's always that question of whether people that are going to blow up airports warn them first...but that's just crazy talk...