Given that the Extra was
Sakakibara's Aunt Reiko Mikami, who was also the assistant homeroom teacher,
and that
everyone's memories and official records are altered.
Is Reiko really related to Sakakibara or was
that a lie fabricated to account for her existence?
Reiko Mikami is the younger sister of Ritsuko Sakakibara (mother of Kouichi), so she really is his relative.
She is the extra because she died once before, which pretty much proves she existed.
Another proof of her being Kouichi's aunt is
Rei, the parrot she hates, was bought by her father after her death and was named after her.
You can also see her flashbacks from when she was a student in the manga.
