I'm wondering is using modern materials would make this easy. Put down straw or other insulation, put pond liner over it, and that might be all you need. Or maybe put a layer of clay over the pond liner to add some heat capacity to it, to allow for a cool surface for which dew can condense.

First of all, they go on to say that other investigations found they did collect water from dew.

Anyway, they're insulated from the earth, via a layer of straw. On top of the straw, a waterproof layer of clay is deposited. The ponds are quite wide and shallow. What happens is the water collects in the pond, and heats up from the sun during the day. The heat doesn't escape very quickly into the earth because it's pretty insulated. Then, at night, the shallow edges of the pond are cooled via evaporative cooling. So you've got a situation where there is a body of warmth in the center surrounded by cold clay. This causes water vapor to condense from the warm air above the pond onto the cold surface around the pond.

That's the technical explanation. On the empirical side, why in the world would somebody make such a pond shape, put a layer of straw down, then spend a lot of time sealing the top with clay to make a waterproof bowl above the straw if it didn't work?