There are apparently ways to legally produce books ABOUT Star Trek (and other media properties) without being authorized but that skirt those requirements. Check out the entries for authors Edward Gross and Mark A Altman on Amazon. They are prolifically publishing guidebooks and other nonfiction works about Star Trek, Battlestar: Galactica, Buffy the Vampire Slayer, Rocky, etc, including photos obviously from the productions themselves, yet all clearly labeled as "unauthorized". They've been doing so for years; I even have a couple I bought in a regular bookstore. So there must be a legal niche for those sorts of works. Some unauthorized and unlicensed material must be able to be sold without being sued. You just need to do it the right way...
But I doubt that a "guidebook" about Axanar, itself an unlicensed fan film, could qualify as an exempted publication.