Derech, doesn’t he preface that paragraph with, “If you believe the letter…”?
The Kasha from Reb Avraham Ben Harambam is a strong one, besides it sure does sound a bit too fantastic. It comes together with Aristotle meeting a Jewish sage and regretting everything, the Gra overhearing a Chassid and changing his mind, Reb Moshe de Leon admitting quietly that he made it all up (at least the parts that he had), among other conspriracy stories some people like conspiracies and some don’t.
I personally have the approach of another conspiracy, that the Rambam knew Kabbalah, like his friend, the ibn Ezra, and as the Raavad assumed he did. Reb Reuven Margalis showed parallels. That’s what the second letter suggests. The Migdal Oz also mentions having seen that second letter, or something similar.