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The news is obviously fake: the main Fox News account says nothing about the shooting, and no other agencies or media outlets are reporting anything of the sort.
This is another one in a long string of hacking incidents which have grown increasingly common in the last couple of months. The group that hacked Fox News' Twitter account doesn't seem to be directly related to the two hacker groups that were in the spotlight lately -- Anonymous and the recently disbanded LulzSec.
Update: We've contacted Fox News, whose spokesperson pointed us to another story saying that their Twitter account has been compromised, but declined to give any further comment at this time.
Furthermore, the @foxnewspolitics account on Twitter has now been erased.