Libertarians did make an actual island, Republic of Minerva, but the Australian/western and Polynesian governments were so scared shitless of a tiny island of libertarians that they concocted a story about it being "Tongan fishing lands" (despite the fact being way out of Tongan waters and Tonga basically ~never having mentioned it until some other people decided to put an island there). Then they sent the Tongan Navy to take it by force.
http://www.queenoftheisles.com/HTML/Republic%20of%20Minerva....
What exactly is the argument for why their credibility should be taken as higher than the Tonga government claims?
Because there clearly could be ulterior motives involved on both sides.
Nothing scares a cartel of coercive monopolies extracting rent from trivial administrative work more than competition.