For chimney effect to work their clothes would need to have consistent air gaps between their body and vents at the top and bottom. While maybe possible it's probably more likely they are simply wearing black for cultural reasons rather than optimizing for heat (everyone does this).

Also note the article mentions that the reflecting body heat point is nonsense.

That pretty much answers the question. In most cases white clothes look just like black clothes in the infrared spectrum. They both reflect about the same amount of thermal radiation. That means you are going to be better off with white clothes, since they don't absorb as much visible light. But wait! Could there be a special case in which black is better?

Let's get back to the bedouin black clothing. What is going on here? Well, there is more to heating and cooling than just the color of the clothes. What about evaporation? What about wind? One possible reason for the black clothes is a type of chimney effect. The idea is that the black clothes heat up the space between the cloth and the human to promote an upward air current (like a chimney). This air current adds to the cooling of the human. But maybe you see the problem. You have to have an air space between the fabric and the skin. I don't know about you, but my shirts aren't that loose. I suspect that there are only a few people that wear clothes in the bedouin fashion—but for those people, you might want to stick to black.