I recently saw a documentary about the Crusades, and during the scene in which Saladin is almost assassinated by the historical order of Assassins, they are portrayed as wearing plain white clothes with red sashes. This is, of course, quite similar to the clothing portrayed in the Assassin's Creed video game series, especially the Crusades-era character, Altaïr Ibn-La'Ahad.
Is there any historical basis for this clothing pattern or color scheme? It seems odd to have both a video game (which is obviously fictional but which famously includes numerous true-history elements) and a genuine documentary about the period share such a specific trait if it wasn't grounded in truth, but then it could also be an in-joke or a playful nod from the costuming department of the documentary.
I can't find anything in my research, but that's mostly because I just end up finding Assassin's Creed-related images and information, not historical. (This is the problem when a historical order has such a generic name.)
Does anyone know if the red/white color scheme has any historical basis from the actual assassins of Persia and Syria? Or was that purely a fabrication for the video game series?