The speaker actually claims it works by "interstitial suspension". I think he is referring to capillary action, which you are aware is involved here. He does not claim this method is faster, only that it is more environment-friendly. Shaking before wiping is a crucial factor.
Folding has 2 advantages : it reduces excess towel at the edges which is not used, and it makes the towel thicker so that the paper between the hands does not become saturated, when it will have no further drying capacity.
Yes, folding twice might be even more effective, depending on the size, thickness and quality of the towel. However, excessive folding leaves paper in the folds usused (ie dry) while the outer surfaces are overused and become saturated. So a single fold might be optimal.
Why not do some personal research and report your findings? (Be quick, or Floris will beat you to it!)