The question is, can fanfiction – sub-writings in a fictional universe, by fans – become Canon, i.e. officially a part of the story?
I myself would err on the side of “no, not really”, without making a categorical claim on it. But more important than the answer to that question is whether a story, any kind of story, follows its own structure consistently.
My last podcast was a discussion of sequels that did not respect established lore. Not fanfiction, mind, but canonical sequels. When people talk of “respecting the fans”, they really mean “respecting the lore” – i.e., not ignoring what has been previously established in order to Subvert Expectations. You can’t just give Bran and Sansa crowns because that feels good and completely ignore the political realities in the published Song of Ice and Fire canon, for example. So for me, the greater question than “can fanfiction become canon/” is “can sequels become canon?” or even “can the later series of a TV show avoid destroying its own canon?”
Wright discusses the points of internal consistency in Part 2 of the essay.