As Marseil pointed out, it is more of a regional custom than a religious one, though they attribute it to religion to give it more force (and so they don't have to explain it). And you probably don't get points for not knowing the difference between a burkah, hijab, or chador.
But I do find it fascinating how fixation on religious surface appearances drives rational thought out the window. For example, this short article mentions a situation near the end:
In brief, when the Shah was put into power in Iran by the U.S, it was a decidedly anti-religious regime that used the same type of brutality to supress it as the religious governments use to enforce it. This woman's grandmother (when she was younger) would wear her chador (head covering) outside, and when the police pulled them off as forbidden, she and other women would lift their skirts and pull them over their heads.
It's hard to imagine the mindset that finds naked hair more embarassing than a bare bottom in public. But there you go.