Charles Johnson's book A General History of Pyracy (short version of the title, full title is much longer) is a significant piece in the realm of pirate history - but how to tell what is fact and what is fiction? The easiest word to summarize this is - Context.

What is the context of Johnson's book? It is a publication in London, published through a man who also published a newspaper that also included a lot of news coverage of pirate history (that helped inform much of the content in Johnson's book), that was targeted and entertaining a larger reading audience. It was published in a time where authors engaged in what literary historians call "factual fiction" - which involves mixing fiction into fact whenever an author found it convenient to do so. Maybe they included fiction to spice up a dull spot in a narrative, or needed to keep the flow of a narrative going, or wanted to drive home a specific message to readers, or didn't have any facts at hand to fill in a gap in a story, or was running out of content and needed more, or a host of other reasons. Crime biographies were a popular trend at the time as well. But there was also the worry of authors presenting untruthful things to their readers (if it wasn't an obvious fiction account - not to mention the issues of libel running rampant at the time, that's another matter I'm not going to cover here), so attaching the word "history" to a text is like attaching the buzz word "accurate" to historical dramatizations on cable today. Johnson's work engaged in "factual fiction", especially the second volume of his work.

How do we know what is fictional and what isn't in Johnson's work? While almost every historian for every period will tell you there is a scarcity of documents (except maybe some cases, especially in the modern era, where there is so many documents - such as World War 2 - that the sheer volume can actually be inhibiting), that doesn't mean there aren't any other accounts. In the past century, especially the last forty years, historians and writers have been catching on and finding that archives are full of documents regarding late seventeenth and early eighteenth-century piracy. Newspaper reports, correspondence between colonial governors and the Board of Trade, letters from Navy captains, depositions recorded by authorities directly from the testimony of the victims of pirates, pirate trial accounts, published travel accounts by those who happened to encounter pirates at sea, and more are all out there. There's been enough research done that historians such as Manuel Schonhorn have identified many of the newspaper accounts and other sources the author of A General History of Pyracy used to write parts of his book (Schonhorn also edited the currently fullest version of Johnson's work, since it includes both volumes and has all the chapters from all four of the editions of the first volume printed in its original runs from 1724-1726).

There is no doubt that parts of Johnson's work are correct - the Bartholomew Roberts chapter in particular. But it's also apparent when he was either lacking documentation and/or made up things to fill content for his work since we now have documentation outside of Johnson to consider. The second volume, where your Libertalia stuff is, particularly is an example of Johnson trying to fill content into his work so he could sell more to his paying readers. For an example of documents showing where Johnson used fiction or lacked documents, look at Samuel Bellamy's chapter in the second volume. Over half of his documented history missing (Johnson pretty much only covers the tail end of his career). There is so little of his documented career in this chapter, that the chapter would have only been a page long if Johnson hadn't expanded on it with fiction. Overall, probably due to his being in London, Johnson's work is pretty poor for any pirate activity before 1718. The newspaper and publication media in London didn't really start publishing heavily on pirate stuff until about 1717 and 1718. As a result, the history of pirates and piracy as a whole in the years 1717, 1716, and earlier is often light, inaccurate, or nonexistent. Why else would some of the more obscure pirates get their own chapters of a few pages each, but not Benjamin Hornigold, John Cockram, or Henry Jennings? Sure, those men receive a mention a couple times in other chapters, but their histories are not told by far. Why? Those three all had pirate careers that fall mostly before 1718. Another example is Blackbeard's early history - which I cover in full detail in this article: The Firsts of Blackbeard. There are plenty of details Johnson gets wrong or are not included in his chapter on Blackbeard for the years of 1716 and 1717.

For Libertalia, several historians have researched and written on this fictional pirate kingdom. None of them have come up with documentation to demonstrate that the place ever existed. Considering the context of where the story came from (Johnson's work, which has factual fiction in it, or sometimes outright fiction - not to mention Libertalia is in the second volume that included more fiction that the first volume), the lack of documentation period documents regarding it, and the period literary tradition of telling stories about pirate kingdoms on Madagascar - there is no sign of the concept of "evidence of absence" being applicable here (or, as you called it, "we're just missing evidence").

As for Thomas Tew, there are current secondary sources that are out there that have footnotes regarding what period primary sources talk about him (that aren't Johnson). I would start out with anything historian Kevin P. McDonald, who wrote a book entitled Pirates, Merchants, Settlers, and Slaves and a couple of articles, “‘A Man of Courage and Activity’: Thomas Tew, Anglo-American Piracy, and the Manhattan to Madagascar Trade Network, 1690-1720,” and “‘A Man of Courage and Activity’: Thomas Tew and Pirate Settlements of the Indo-Atlantic Trade World, 1645-1730.” (2005). Also, Mark G. Hanna's Pirate Nests and the Rise of the British Empire, 1570-1740 will have footnotes that will help as well. That is the key to doing research like this, you dig through notes of other historians to get an understanding of the historiography of a subject and to dig down to the period sources that is the foundation of understanding said subject.