It would be weird if the OTW just outright stated that fanfiction was copyright infringement, starting off from the position of "yeah, it breaks the law" would be a bad form of advocatory. The case they link on that FAQ is about a parody of (at the time) 20 year old song, which is materially very different from how fanfiction works. I do think if it ever did go to court that a non-commercial exception would likely be carved out, but as it currently stands I don't think there's any precedent in either my own country or America that can be used to argue that fanfiction meets the criteria for fair use/dealings. Then again, I'm not a lawyer so my opinion probably isn't worth much.
(sidenote: it's mad that American copyright law doesn't have an explicit exception for parody)