Sounds like a variation on the explanation of why Bedouins living in the arid, scorching desert typically wear heavy, dark robes. Some scientists did some research and found that although the skin temperature of people wearing light and dark colored robes were similar, those wearing dark robes felt more comfortable.

The reason why dark robes feel more comfortable is because, first, the dark robes are worn over a second, lighter layer. The dark robes absorb sunlight, heat the air trapped beneath them, then the air rises through the garment as convection currents. As the warm air rises, it draws somewhat cooler air through the bottom of the robe, and that air flow helps evaporate the sweat that is soaking the inner layer and on the skin. Thus, you end up with a drier layer of clothing next to your skin, plus the cooling effect of evaporation. With light colored clothes, the outer layer will reflect the sun's rays, but that does nothing (or does less than a dark color) to enhance the evaporation of sweat from the fabric or the skin, so you end up with a clammier feeling garment even if the the light colored exterior reflects more of the sun's rays. Pretty slick, eh?

However, while that principle may work for personal robes while sitting quietly or moving slowly in an arid environment, I'm doubtful that you could generate strong enough convection currents from some sort of tarp shelter to make any difference to the people taking shelter under it, like some sort of natural air conditioning system. That just doesn't seem possible.