This depends, of course, entirely on what your definition of fic is.
I've read enough on the subject to learn that, like any definition, it's malleable----changing with context, groups, time, and the introduction of new technology. For most, fic is as Karen Hellekson and Kristina Busse define it: transformative works that use someone else's characters and worlds as a starting point for the piece. However, right there are a number of assumptions that complicate what fanfiction supposedly is. Is it primarily written in English (given the historical influence of the Western canon and English-speaking scholars like Jenkins and Camille Bacon-Smith)? Does the "piece" need to be textual (as opposed to fanvids or GIF-sets that tell similar stories)? Is fic primarily serialized (what if you post all at once?), should it be considered non-commercial (excluding tie-in novels or commissioned works)? And does it require the communal interaction that so many scholars have emphasized? Is it still fic if no one ever reviews your work or no one even reads it?
Still others raise more, potentially crucial concerns:
Noah Berlatsky says that fanfiction is far more than just amateur, non-profit literature. Fic is not merely a fan's response to official works, but is crucially often better than what came before it.
Gerry Canavan wrote an article exploring authors who are very open about their "borrowing" of others' work, yet they consider themselves distinct from fanfic authors. For example, Lev Grossman wrote The Magicians as an "adult take on the Hogwarts mythos" and openly draws from Rowling's series, yet he's not entirely comfortable with the label of fic author.
A fan included in Pugh's book The Democratic Genre redefines the term "serial novel" to describe stories that, while able to stand alone, possess similarities to other works that need to be acknowledged, thereby merging concepts of "fanfiction" with more mainstream categories.
Pugh herself says that it's the inclusion of shared knowledge within a community that makes fanfiction fanfiction.
Francesca Coppa, meanwhile, says that we can "define fan fiction as a textual attempt to make certain characters 'perform' according to different behavioral strips," thus highlighting fic's transformative capabilities.
Robin Hobb in her infamous Fan Fiction Rant says that fic is any fiction "written by a 'fan' or reader without the consent of the original author, yet using that author's characters and world." Thus for Hobb, the creation of fanfiction is in direct conflict with the definition of a ("real") fan and supposedly it's not fic if the author gives you the a-okay.
And Cornel Sandvoss emphasizes that fanfiction is all about variety and instability. If your text is a fixed piece, it's not fanfiction.
These concerns have come to the forefront of fandom conversations in recent years. Did Cassandra Claire discover a line between fanfiction and plagiarism with her infamous Draco trilogy? Is Fifty Shades still fic or something between mainstream and transformative work? Is Anthony Horowitz's The House of Silk a pastiche with more merit because it's endorsed by Doyle's estate? That comment at Loock's presentation----are reboots and spinoffs reflective of online fanfiction?----draws a number of these questions together.
Though I didn't get the chance to voice my opinion then, I'll do so now. No, I'm not sure these texts should "count" as fic. They do, admittedly, fit within fic's broadest definition. A spinoff or reboot airing years after a show's original run is a transformative piece that most likely is created by someone other than the original author(s) of the show. However, that's largely where the similarities end.
Television shows are not textually based. They are commercially driven projects. They are controlled by people already in a position of cultural power----and that right there (for me) is the kicker. A spinoff or reboot, no matter how inventive, simply does not have the creative freedom that online fanfiction allows. Another commenter at Loock's talk noted that continuations of shows like Full House or Gilmore Girls are the only way that producers can easily get away with all or nearly all-white casts, eliminating our recent strives for diversity on the small screen. And she's absolutely right. At least in terms of race, television tends to keep the original status-quo, with only a few exceptions like characters who's ability to change physically are a part of the core narrative (like the Doctor - even though he remains pretty white... ) or series that span generations (like Star Trek: Discovery). Though there are always exceptions to the rule, television works to recapture old and new audiences alike by providing viewers with characters they can easily recognize.
Not so with fanfiction. Fic authors make various social, cultural, and biological changes all the time. For many, progress and possibility are not necessarily in conflict with the core personality of a character: what allows us to recognize and continue to love them. Who's to say that your favorite can't discover that they're gay in their late forties? Or become disabled? Or that they weren't black this entire time? Such arguments are often easier when it comes to novels, a medium that is primarily imaginative rather than visual. It's how we got a black Hermione for Cursed Child----the novels never explicitly stated her race. However, this difficulty when it comes to television----viewers' need to recognize their characters, often a key factor in obtaining reboot viewership----limits the show's possibilities in ways that go beyond logistical considerations like budget, scheduling, etc. Fic simply has more ground to do more work with fewer potential consequences.
All of which doesn't even touch on other major characteristics like fic's surrounding communities, crafting stories in response to reader feedback or working within the constraints of a challenge. Do reboots and other shows engage with fan reactions to their work or craft episodes that play within certain boundaries and limitations? Of course. Just look to Supernatural for examples of both ("Fan Fiction." "Bitten.") However, these kind of episodes remain the exception rather than the norm. In the interest of acknowledging that we sometimes have to limit language in order to keep it useful, "fanfiction" should not be applied to rebooted, re-made, or spinoff shows that are produced by major networks. In the same way that though we might yell that the Aeneid is fanfiction as a way of establishing credibility ("Hey, we've always been here!"), it's not the kind of "fanfiction" we're usually talking about.
After all, given its massively broad definition, nearly anything can be fanfiction if allowed enough leeway.
“Only those with no memory insist on their originality.”
- Coco Chanel