I think the interest in purportedly true stories is a natural one. Travelers’ tales have always been with us, and still are (e.g., the perennial school essay, “What I did on my summer vacation”). It was perfectly reasonable for people in ancient times to want to know what was on the other side of the mountain, due to curiosity, avarice, or fear. Today many people enjoy hearing about other people’s travels because it offers an enjoyable vicarious experience. It has spawned a whole genre of travel books. No doubt some of these narratives contain lies, which, leaving aside the moral objection, may or may not matter depending on what the reader wants from the story. Many people enjoy the experience of the mysterious, which Einstein called the most beautiful thing, regardless of whether or not it is true. This is mainly why we have science fiction and fantasy stories, I believe.
We have, contemporary with Lucian, Apuleius’ The Golden Ass, a tremendous fantasy novel that makes no pretense of truth IIRC, or at lease no credible or serious pretense.
Lucian’s main target was Herodotus. He has been followed in his critique by many modern commentators, who all bizarrely ignore Herodotus’ disclaimer that the things he related were mostly what he had been told by natives, not his own experiences. It is clear today that Herodotus should more justly be called the “Father of Folklore” rather than the Father of History.” I don’t regard that as a demotion, by the way.
As to the pretense of truth in fictional narratives, this is merely a technique for enhancing verisimilitude, as is the use of first-person voice. Some decades ago, lit crit and writing seminars were advocating the use of brand names to enhance verisimilitude. Don’t say “I quickly ate breakfast,” say “I shoveled down the Cheerios.” (I wonder whether any authors ever solicited brand placement payments like the movies do.) Thankfully this use of fake realism seems to be fading. Whether a general claim of truth is useful, I don’t know, but certainly true, accurate locations are useful, especially in genres like thrillers or spy stories.
I think all realistic fiction has an inherent claim of truth, so I am not bothered by details or explicit claims to enhance that. Writers, after all, are typically advised to write from experience. If we were sitting around the fire 10,000 years ago, and the storyteller went to work, we might not know whether he was telling a true story. This is still true in George Borrow’s Lavengro, Jack London’s Martin Eden, and many other works that combine personal history with fiction.