I found this really interesting especially because I was talking about the whole TCC as fanfic thing with my spouse last night and, one of the things we were talking about was authors writing stories that are not fanfic (because-as you rightly point out-they’re the authors), but that function as fanfic in how they elaborate, reframe, and reinvent the earlier works. Carry On came up, as did Lois McMaster Bujold’s Gentleman Jole and the Red Queen (which has also been accused of being fanfiction probably because it focuses on building relationships and romance). Both are stories that don’t simply continue previous works of fiction, but reframe hte reader’s understanding of them without actually touching any of the events in the original. (Whether Carry On responds to Fangirl or HP is probably a matter of debate, but I do think that Rowell’s book is a fictional critique of Harry and Dumbledore’s relationship at the very least. If it’s fanfic, it’s fanfic in the style of John Milton, which is a whole nother can of worms.)
I like this trend — I think there’s real value in sequels that respond to the earlier stories and if fanfiction is not merely a medium, but a genre as well, then it should have a set of familiar tropes and styles that can leave the genre and call back to its original form from a new text. But then — is fanfic a medium or a genre?