Remember, any inaccuracies are either because of the animus(either a glitch or because it was programmed that way) or because the Templars rewrote the history books for reasons, even in cases where it would make the assassins look bad, incompetent or like assholes.I can totally see that, but at least they have the taste to call them The Hidden Ones and the Order of the Ancients instead. I mean, Valhalla is very far from historically accurate and makes quite a show of it. About half the major cast are women in leadership roles (and most kick major ass) and there are quite a few supporting characters that are PoC, including one person of indeterminate Asian Steppe origin and a hunter that seems to be from the Levant. Valhalla is playing fast and loose with its history, but it doesn't really make any claims to being historically accurate and the game is much more colorful and better for it.
Also, books are dumb and you shouldn't believe them.