One stumbling block (for me) to consider it to be art is the fact that the stories do not stand alone.
sartorias says it so clearly here, "Thanks for that suggestion. I think I need to read/watch before I can read this . . . I started to, but there are too many things assumed that are unfamiliar to me."
Now, in my view (and I'm not saying that my view has any validity other than it's my own opinion wot I thought up all by myself), a story (or in fact any artwork) should stand alone[*]. That's what I tell the students I teach on the creative writing course Start Writing Fiction. I point out that the writer is not there to explain bits of description, plot or necessary background that has been omitted, nor to tell the reader what the story is really about.
It all has to be in the story, and in fan fiction, it isn't.
Now there are writers who write series -- murder mysteries, SF and fantasies often become a series -- and I admit that if you read all the Brother Cadfael books in order you will get more out of one from near the end of the series than if you hadn't. But it will still make perfect sense if, as a new reader, you read late book first rather than starting at book one. Ditto a series like Lois McMaster Bujold's Miles series. Bujold doesn't assume that you've read the early books when she writes the next in the series. She can't. Publishers have a habit of letting early novels go out of print so sometimes the fifth book might be the first that a reader encounters in the bookshop.
A large part of the skill of a writer of ongoing series is deciding how much backstory to include and how to insert it into the story in such a way that it is still interesting to the keen fan who has read all previous volumes, possibly more than once and will still provide the essential knowledge that a new reader needs.
Fan fiction writers, however, don't bother to learn how to do this because they know they don't have to. They have a clearly defined readership and can assume that everyone reading the story already knows what Harry Potter, Snape, Arthur or Merlin looks like. Ditto the setting. There is usually a comment to introduce the story that tells the reader that the story fits between Episodes X and Y and that's it. In other words, fan fiction readers and writers are playing and having a great time amusing one another, but they're not creating a story that will stand on it's own and that could be read and understood by a general reader who had never followed any of the source material. Neither will the story still make sense in 50 years time when the originals that inspired them are forgotten.
In case this all sounds rather po-faced, there is a sort of derivative creativity that I enjoy a lot and that's parody. But a good parody also stands alone. Take for example one of my favourite films "Galaxy Quest". Yes, it's sending up Star Trek like mad, but it works as a film in its own right. If you'd never watched Star Trek and only had a vague idea of what it was about, "Galaxy Quest" still works. Pratchett's Discworld stories are in one sense derivative in that they draw for their inspiration on many different aspects of our world, but you can still enjoy and understand Wyrd Sisters even if you've never read Macbeth. Yes, you get more out of the book if you can pick up the references and Soul Music is not one of my favourites, partly because I suspect I'm missing a lot of the jokes due to never having been a fan of rock music of the right era, but it was still possible to read and enjoy it.
Now, it could be that I just haven't read enough good fan fiction and as I don't have time to read all the published books that I have already bought, more reading material is not high on the list of priorities, but if anyone can point me to a fan fiction story that they consider good and that stands alone and works even for people who have no knowledge of the source fandoms, then I'll be happy to revise my opinion.
[*] Sometimes a 'novel' doesn't stand alone, but that's because it is actually a volume out of a trilogy, but in that case, I submit that it isn't a story, only part of one despite the recent habit of publishers of publishing trilogies without admitting up front that that it what they are.
ETA: zeborahnz has pointed out here that all writers assume a certain amount of background knowledge, which is true. There are expectations placed on the reader that a lot of stuff doesn't have to be explained and it's why old stories start to need footnotes to explain the things that are no longer part of our culture. On the other hand, I've never heard anyone say, "That story sounds really interesting but I need to read up about the Wars of the Roses before I can understand it," so we're talking about a different level of specialised knowledge that's required, which as I said above, rules out the general reader. zeborahnz has also provided a link to at least one story that I felt did standalone, so I'm happy to admit that I might have been generalising on too small a sample. (Haven't had time to read the others yet.)
I'm also still pondering whether I would count the works listed here as fanfic. Personally I wouldn't, though I can see why some people would. However, as far as I know, they all pass my test of standing alone, so are in the running to be considered as art. Note: Just because something has won some high falutin' literary prize doesn't necessarily mean that I personally will like it or think it good. :)