Been thinking more about this. What makes it [fanfic] not public is the attempt to fly under the radar of the Powers That Be, right? Or at least not actively draw their attention? Though how much that's done varies quite a bit from creator to creator. I know of at least one mailing list, read and posted to by the author, where fanfic is simply labeled "fanfic" so she can avoid reading it, but there's no attempt to pretend that it doesn't exist.
I've been thinking more about it as well. This is less an answer to your question than it started out being, but it is a more methodical examination of my own reaction.
What makes it less public is twofold, for me. Radar is part of it, but not by any means the whole. Let me try to express it. Let me take a whole new post to do it, because I've outrun my word limit. Again.
Fanfic is not a critique, nor is it a review of what exists; fanfic writers are certainly capable of doing book critiques/reviews or movie/tv critiques/reviews, but no one calls those fanfic. Both critique and review consider the text at hand (or the show at hand), assessing what's there, and giving their (hopefully but not always) informed opinion on it. There is a dialogue of sorts between some of these reviewers and the creative person(s) at the other end; there is a dialogue of sorts between some of these reviewers and the fans of the work in question. But if the review has some heat or love at its heart, it's still about the work as a whole. I don't consider this a dialogue in the standard sense; I'm now using dialogue in the sense that you used it originally, so if I stumble in that, bear with me.
In some instances, I think there are parodies or even satires -- but I don't consider those to be fanfic, and this could be because my definition is way the heck too narrow, i.e. I'm ignorant. Parody usually reflects the original work as a whole, and some understanding of the original is necessary in order for the parody to work at all; I consider parody a broad commentary, because that's the point of parody. Well, and also to make fun of the audience reaction. Digression.
Fanfic, rather than being a (theoretically) objective form of that dialogue or response, is much more of an emotional dialogue; it exists first between the reader and what they draw out of the primary work, and second, in the text they create. It explores other possibilities and permutations (if I understand what you've said correctly) that the original work did not -- or hasn't yet. Or never will.
But much of fanfic is essentially fiction, with serial numbers, and its aim is the aim, in many ways, of the original work, because if it didn't have some of that same feel or tone it wouldn't be fanfic. Because of the serial numbers, there is a need to fly under the radar. I would argue that it's that need that allows fanfic to thrive, although it does keep it out of the public eye to a greater or lesser extent. If you don't know anything about it, it's invisible; once you do, it's everywhere. Okay, I really have to stop with the digressions.
Having said that, let's go back to the need to fly under the radar. This is partly necessitated by legal convention, and as the copyright holder, I cannot outright decry it, for a variety of reasons, one being, I have some attachment to my copyright.
What happens under the radar is of less concern to me than what happens above the radar. There are things I would not want my characters to say or do. Obviously, when I'm writing, I have say in this (although, creative process being what it is, not 100% <wry g>). If someone is writing fanfic based on my characters or in my universe, what they want the characters to do is part of their emotional response. And -- beneath the radar -- this is a valid exploration; it's a little like daydreaming in public, which, in many ways, is where the heart of many stories start. The work comes after.
But if you remove the protective layer, which we'll call the radar level, I would feel a lot more ambivalent, because there are ways in which I would not want my characters to be represented to my readers, many of whom still don't own computers (I know, I always find this a bit shocking; it's stranger, to me, than not owning a telephone or a television but I digress, as always). In the public sense -- in the way my vision is present as my vision to the universe, or the small slice that reads my books <wry g>, and speaking with no delusions of grandeur (although I can't speak for other types of delusions), I can clearly state that I want my vision of my creation to be the canonical vision. I realize that's a lot of genetive use there.
Let me sum it up in a less unwieldy fashion: I do not want other writers defining canon in a universe I create.
But part of the difference in my reaction, part of the sense of "public" or "legitimate" stems, in part, from the medium through which the original property is first presented. Joss Whedon approves of fanfic, but he's doing Television, and I bet he'd be a lot less happy if fanfic writers were to get together and produce and air their own version of Buffy. A lot, as in lawsuits and really ugly things, and I don't think he'd be hands-off at that point.
Many of the people who watch the show will never read the licensed spinoffs, and they'll also never read the fanfic. Both the spinoffs and the fanfic fill a smaller role than the original broadcast did. It's accepted that what happens in the textual presentations or the comic books or the fanfic, etc, licensed or not., are not canonical; they can be ignored or changed or overturned at the whim of the licensor. In a sense, the spirit of generosity that allows the fanfic to exist can only be generous, in my view, because of that -- the other works are not canonical. They don't change anything. They don't touch or mark or move the original, and they don't open or close the avenues the original series can move in. The creator feels free to ignore them entirely.
When you're dealing with fanfic based on written work, you're suddenly dealing with the exact same medium, which is why I think more tension exists.
I don't know any writers who hate filksongs inspired by their works. I don't know any writers who hate art inspired by their work. Or costumes. Many would be perfectly happy to have RPGs or Television shows based on their works (if they were paid <g>).
But none of these media are the primary medium for the creator -- the text, in the case of books, is.
Knowing that canon is decided by me (and knowing that some people won't always be happy with the decisions I make) gives me the same comfort zone that someone producing television shows would have. Reviews, critiques-- these don't really change the way people view the original. Are they public? Yes. But in some sense they relate to the canonical work.
They make no attempt to change the work; they can savage it, they can praise it, they can dissect it for meaning -- but they're not there to rework to it; at most, they can shift the way we view what's already there. In this sense, the work is the point of the discourse. And as all writers know, once something is published, it's public, and people can say whatever the want about it. We're prepared for that. That's the sense of "public" I assume when I see the word.
In the case of fanfic, the work is the stepping stone, the foundation, the thing people stand on while they branch out; the anchor to which they tie their own skills, developing their own voices and abilities. At this point in time, one can sort of assume that readers and writers of fanfic have read or watched the originals, so there's a certainty of informed creation, even if the creation is not canon.
But were the fanfic based on novels to be published as novels in their own right -- without any vetting or interference from the original author -- there's no guarantee that new readers would be so informed, and the canonical understanding of a creation that originated elsewhere -- like, say, me -- could shift radically. A book, after all, is a book, and it sits on the shelf, like other books.
And I'm sorry if it makes me sound hideously selfish -- and I'm aware that it probably does -- but the right to set canon is incredibly important to me.