The threat is part of a larger Anonymous response to the federal raids that shut down file-storage/file-exchange site MegaUpload in January, after which Anonymous hacked or DDOSed the FBI, Dept. of Homeland Security and a range of other agencies of the federal government.
The Facebook attack in particular was derided as a fake by Anon members, though "fake" is relative when it comes to Anonymous. A previous threat to attack Facebook on Guy Fawkes Day was also "fake," because it was sponsored by only a small group of Anonymi, not a plurality of Anon participants or the core leadership groups.
There's no real telling if OpBlackout's targeting of root DNS servers is a similar fake, but it's an ambitious threat, considering the heavy bandwidth-management, security, traffic-filtering, backup, failover and other techniques used by DNS providers to make sure the servers are always available.
SANS Institute warned in 2002 that the root DNS server network was supremely vulnerable, a situation not substantially improved by April, 2011 when attacks on DNS servers affected hundreds of major sites.
Kill the Internet, wound it or just make it worry?
The Feb. 12 announcement described the tool it would use to attack DNS servers as a "Reflective DNS Amplification DDoS tool" based on the DHN tool from the AntiSec movement within Anonymous.
Both tools may be real and formidable; both or either may be fictional, as was the successor to the Low Orbit Ion Cannon (LOIC) Anonymous announced just before the OccupyWallStreet protest began; Occupy was real, the LOIC successor was fiction.
The AntiSec DHN tool is described in some detail here, but might still be wholly or partially fictional.
Anonymous, from YouTube