User blog comment:MyProjectAlicization/Kuroyukihime - Kirito and Asuna's daughter?/@comment-202.156.9.10-20131125063207/@comment-24034641-20131125110226

Reki never stated that, he said that the worlds are connected (in the L.N, Anime AND Manga these connections are seen) as well as the characters being mentioned (Kirito is mentioned by Black Vise)

and also, that forum is only about her real name, not much about her family.