Libertalia was made up. The whole Chapter on Captain Mission in Charles Johnson's General History of Pyracy, the 2nd volume that contained that chapter published in 1728 (the 1st volume published in 4 editions up to that point), has been proven to be a complete fiction. The second volume of that work, trying to exploit the success of the 1st volume, pushed the concept of "factual fiction" even farther to put in more stories to entertain the public. The only part of that story that has any truth is that Thomas Tew was a real pirate that sailed the Indian Ocean.

The idea of the pirate being a purposeful anarchist...I've never seen it lead anywhere in academic study. You'll get attempts at saying they were anti-capitalists, socialists of sorts, or full fledged Jacobites (rather than just believing in it, but not being extremely active for the cause); but not anarchists. Evidence will easily support that the crime for profit aspect of piracy was the strongest and most dominating aspect of pirate motivation. It may have not been the only one for the individual pirate, but overall it was the biggest and strongest. The desire of some modern people to turn them into libertines, socialists, anti-capitalists, and anarchists speaks much more about people today than the pirates (not saying the original poster is trying, his question appears to be a legitimate inquiry).