This is not the full explanation, as can be checked with a simple experiment. Dip a piece of cloth in a glass of water and hold it there submerged beneath the surface. The submerged part will still look darker than the dry part, despite the fact that there is no film of water covering it.
Other comments here have put forward the explanation that the water matches the index of refraction of the material much more closely, meaning that light is more likely to pass straight through the material instead of bouncing off. This explanation seems much more likely to be correct to me.
Another experiment: Put some wet spots on a cloth and hold it up to a light source. More light will pass through the wet spots than the dry cloth. This certainly suggests that the reason wet cloth reflects less light is because more is passing through. (I have tried both these experiments with paper towel used as the cloth.)
Other comments here have put forward the explanation that the water matches the index of refraction of the material much more closely, meaning that light is more likely to pass straight through the material instead of bouncing off. This explanation seems much more likely to be correct to me.
Another experiment: Put some wet spots on a cloth and hold it up to a light source. More light will pass through the wet spots than the dry cloth. This certainly suggests that the reason wet cloth reflects less light is because more is passing through. (I have tried both these experiments with paper towel used as the cloth.)