One thing to watch for, in terms of gaining and maintaining reader or audience confidence is expectations set by genre. Work will be accepted within the context of how it is categorized and the precedents that have been established.
Obviously, a documentary or something explicitly categorized as nonfiction is best treated journalistically. However, there can be variations based on other information, such as the reputation of the work's creator. For instance, ever since Michael Moore produced Roger and Me, the expectation has been his facts will be shaped for a specific perspective (his argument) and much of what is presented will be there to provide humor.
There are many works that are "based on a true story," and these are assumed to be truthful about most of the elements. They often borrow credibility from the audience’s recognition of accepted facts, places, and incidents. The writers who take their stories away from what's documented may tag their works as "inspired by" true stories, which keeps the audience by providing that designation as a caveat. It's worth noting that some people can't tolerate any playful or dramatic responses to reality, but I suspect most people can. No one wants to be deceived, but most people are willing to make allowances for a tale well told. I love the interweaving of fact and fiction in Doctorow’s Ragtime, but I know people who find experiencing it (as a book, a movie, or play) frustrating.
Closely akin to nonfiction is the roman à clef, a genre where characters and incidents parallel those in real life, often with the implication that a straight, nonfiction treatment would lead to a lawsuit. I remember when the movie Seven Days in May came out how people in Washington DC speculated about who the characters might represent in real life. That was part of the fun.
Hard science fiction builds a case for using facts and extrapolating them with as much logic andveracity as its authors can manage. The joy for readers comes from creating a future that both evokes wonder and seems possible, given current knowledge. The Andromeda Strain goes so far as to provide footnotes throughout for journal articles and other references, many of which actually exists.
Film provides an interesting way to pull the viewer in – including real footage. This can be as simple as showing a city. (I love the way West Side Story opens with the view from above of New York.) Spielberg's Saving Private Ryan provides an interesting use of sources by incorporating the visual style (though not the actual shots) of Omaha Beach newsreel footage into its D-Day landing scene.
There are inside story works that purport to show unknown details of our world or culture. Arthur Hailey's novel, Hotel, presents the inner workings of the administration, management, and goals of the hotel. He did a whole series like this, e.g., Wheels and Airport. James Michener’s novels often took this to the limit, sometimes beginning with the geology of a region before finally settling into characters and story.
Similarly, there is a de facto genre around what I call first testimonies. As the culture has opened up to silence their voices – different genders, ethnic groups, classes, religions, etc. — novels that explore the experiences of people pushed out of the mainstream or forced into hiding have presented views taken to be authentic. Often, the credence comes from a level of courage that seems to be present in works that risk disparagement or rejection. Anyone "outing" him or herself is likely to be believed.
In an odd way, commonly can have an authenticity created by its not being taken seriously. My cousin comedian Barry Crimmins said humor was a way to "smuggle in truth." Credibility slips in sideways.
Things can be turned in another direction where facts may evolve into something unexpected, a kind of a con game. If you haven't seen Orson Welles's film, F for Fake, check it out. It's entertaining and provides insights with such wit I can't bring myself to spoil it here.
For me, the most effective path to authenticity has always been presenting a familiar and easy to identify with world with nothing outsized, and managing to presents truth through the characters (sometimes called “kitchen sink dramas”). From the very beginning Paddy Chayefsky's Marty quietly endears me to its characters, and it presents challenges that are completely believable and resonant.
The above examples rely on a variety of touch points for authenticity – journalism, common knowledge, characters that ring true, logic, sharing the secrets, the standing of the creator, and more. As with all genres, the secret to a writer's success is doing the homework. Reading through novels or watching films that are comparable to the work in progress and looking to see how authenticity is achieved (or what leads to artistic failure) is vital. So, analyzing work that's out there and noting the tools that bring credibility, along with how much deviation an audience might tolerate, is a great way to bring authenticity to your work.