If Sony keeps doing it, their documents will be forever alive in the form of magnet links, formerly torrent file sharing technology.
Regardless, those documents will be floating around torrent sites, even if they do nothing. The horse has left the barn.
But this isn't about trying to actually keep the information under wraps - this is about trying to get some financial recompense. Like, someone let the horse out, and your neighbor suddenly has a sale on fresh horse meat... You're not getting your horse back, but maybe you should get a portion of their unlawfully gained profits.
In particular, the material includes both material under copyright, as well as trade secrets. Copyright law doesn't include a safe harbor for "but I'm a newspaper" or a generic "first amendment!" defense - while papers could publish short excerpts of the leaked info under fair use (17 USC 107), for news or commentary purposes, they could not, say, publish the entire script to the new Bond movie, relying on a defense of "well, we didn't steal it, and the first amendment says we can publish anything we want because we're the media."
Going further, many states' trade secret laws actually include explicit provisions about publishing trade secrets that were obtained unlawfully, even if you weren't the person who originally stole them. And while terrible law professor Eugene Volokh thinks that the Bartnicki case has a first amendment exemption, he's clearly never actually read it - SCOTUS specifically said that it doesn't apply to trade secrets, but for matters of public interest. Now, that may apply to things like Sony's CEO's salary, but it likely doesn't apply to things like advertising campaign plans or product release strategies.
So, if the media publishes the unlawfully obtained trade secrets or publishes the material under copyright in a way that exceeds the bounds of fair use, then they may be financially liable for Sony's damages. That doesn't put the horse back in the barn, since it's gone, man, but it does at least help pay for the new horse (and maybe a better lock).