Yes, that's precisely the part I was addressing in my last paragraph. If it's specular reflection, then in "most directions" it will appear darker, as you say, but in one direction it should appear brighter, even shiny. But I've never seen a damp rag be shiny in any direction.
(...and it shouldn't be that hard to see, if that effect is really true. With any other shiny object (polished car, CD, balloon) you see the specular reflection frequently.)