If anything, HF is the ending to the story supplied, but I refuse to believe it as the final ending. It does not fit with Nasu's writings.
The thing I see across Nasu's works a lot is the protagonist having to deal with, and accept, himself/herself for who/what they really are and it leaves them with an outlook on life where they confront their past/future/alternate self, and decide or plan on how to live their life based on that.
Spoiler for Tsuki, Fate, KnK spoilers:
Spoiler for Tsukihime spoiler:
In Tsukihime, Shiki has to deal with the growing impulses leading to murder and such within himself. Sure they are not his own feelings, but they are transmitted through himself. Whether it be dealing with the Nanaya impulses or the Roa impulses. I mean, in the Near Side of the Moon, Shiki loses himself and rapes Kohaku because of the impulse...when attacked by the Dead in Arc's route, when she is pinned he loses himself because he refuses to allow the Dead to 'spoil' Arc saying that she is his alone. In the Far Side, he completely becomes bedridden and cannot even move because of this. Overall, the main story to Tsukihime is Shiki dealing with his alternate self whether it be Roa or Nanaya and overcoming it.
Also, in Kohaku's route, it may end happy but the road there is nothing happy at all. Hell, Kohaku even dies and forgets her past self and ends up being reborn leaving everything she had behind and becomes "Nanaya" because of the pain the name Kohaku gives her.
Spoiler for Kara no Kyoukai spoiler:
In Kara no Kyoukai, Shiki Ryougi is two personalities, one male one female. When she is in a coma, the male side of her dies/abandons the female part of her. To cope with the loss, even though her personality is female she talks with masculine wording using "boku" instead of "watashi" and others to make up for the loss. In addition, the entire story she believes herself to be a killer when in fact she is not. At the end when she finds out that Lio 'kills' Kokutou, she loses herself and stands dumbstruck while Lio attacks her.
Remembering Kokutou's final words about her not being a killer because she already knows the pain of death, she unconsciously kills Lio. When she realizes this, she is left paralyzed realizing she actually took a life. Even though she forced herself that she was a murderer, the reality of it shook her and left her scarred. Kokutou lives and they end up in a hospital with the ending that Kokutou would be there for her even though she did commit a murder it ends. There is an ending/epilogue called Gospel in the Future, but I personally cannot see that as canon with the story. Shiki is left in Kokutou's care so she turns out for the best despite her broken will. (I see this as linked to UBW because Archer leaves Shirou in Rin's care so he turns out for the best and so he won't turn out like Archer).
In Fate, well as this is the Fate board, there is nothing I really need to say about the protagonist dealing with himself as an antagonistic force.
I will admit that Notes was listed as merely as a mini-story. It appeared as a doujin work within a compilation of other works so it cannot be seen as a full work. However, it does provide the basis for the Nasuverse albeit being set in a future setting more than 3000 yrs in the future from F/SN, Tsuki, KnK.
In HF, Shirou realizes it at the end who Archer is but as to why Archer is there or what relation Archer has to himself, there is no recognition.
Now this is contradictory to what I've been saying, but I do see the UBW ending as a happy ending. Everything is resolved, the Grail War was not intended to be completely resolved in UBW but just ended for the time being. Shirou knows his possible future and has Rin to keep him on a path away from that ending. Despite this being as happy as it is, I see this as being an ending to Fate.
I don't see Fate as being a closed story, but rather an open-ended question. This is Shirou's life, this is his fate...how is he going to live his life from here on? Simply put, the paths of Fate and UBW put forth this question. There is no doubt, the game even states such. It also says that a possible ending is HF, that said it also says that it is the final ending to the Fate story.
If you guys believe HF to be the only answer to the question, or the correct answer, that is on you to believe the wording however you want to. I'm just saying I don't believe it to be and there is no way you can convince me otherwise. I will admit it is a possible ending, a rather forced and really stretched ending, but an ending. I will not admit it as being the only ending nor the correct ending. Go ahead and provide whatever clues you may throw out, but as the story is written as it is, there are far too many inconsistencies and quirks to HF that is so unlike Nasu's other works that I will not believe it to be an ending he truly intended.