I'd also like an answer to this one. It seems like most of these explanations would also apply to plastic or metal getting wet, so why does cloth get so much darker than other materials?

It feels like the fact that water is absorbed has to matter here--wood, dirt, cloth and sand all darken when they absorb water but not when the water remains in a bubble on the surface (as it does on cloth/sand/wood treated with a hydrophobic coating).