The character reputation data displayed on the reputation calculator is made available by Blizzard by a public facing api. As a result, myself, and other developers, are limited to the data that Blizzard returns from these various end points. For the most part, the api is sufficient. When you provide the api with a character, a realm, and a region, it will give you back the reputation data for that character.
However, there are a few known bugs with the api. Most notably, several factions are missing from the data returned from the api. Both of the Pandaren factions (Tushui and Huojin) are not present in the data returned. Also missing from the Mists of Pandaria are the Pearlfin Jinyu and Forest Hozen. Introduced in the Throne of Thunder patch, Emperor Shaohao is also missing. The only non-Mists of Pandaria faction missing are the Knights of the Ebon Blade, missing from the Wrath of the Lich King expansion.
What’s interesting is the idea that all but one of the problematic factions were introduced in the Mists of Pandaria. My theory is that this api was constructed around the same time and given that Blizzard doesn’t make any direct money off of this, they haven’t been inclined to fix it.