That is a valid line of reasoning that arrives at the same conclusion, but it's not the reasoning put forth in the fic.
The sex change alone does suffice, and the line of reasoning used in the fic would make no sense if the character's sex were not new.
For the past two months, I've been writing, and posting, roughly two thousand words a day of "Myou've Gotta be Kidding Me", a story set in a "My Little Pony: Friendship is Magic" fanfic universe, "Chess Game of the Gods". Outside of the sheer NaNoWriMo-like exercise of pushing out near-daily chapters, I've also been trying to keep in mind the various principles I've learned from Yudkowsky and LessWrong, and to try to present them in a way that people who like reading MLP fanfics might be able to appreciate.
I've just come to something of a minor climax with chapter 60, and while I'll definitely be continuing the story, this seems like a good time to mention it here, for whatever feedback and constructive criticism anyone cares to offer.