IIRC, Aladdin was originally told by Muslims, but it takes place in China. It is about as "accurate" as you would expect from stories told about China by a Persian villager around 1000 AD, which is to say, not very. China did not have a caliph, for example.
(Ninja'd, sort of.)
Offhand, I can think of only one adaption that set Aladdin in China. It's on Rifftrax.
Also, Aladdin is not part of the 1001 Nights stories. The volume that originally (or nearly so) that brought these stories to the West was titled 1001 Nights and Other Stories. Aladdin was one of the Other stories.