I think it is true and untrue just like with yogurt.
Generally thicker yogurt is better because it was fermented longer, but knowing this, cheap yogurt makers add thickeners. 

With soaps, in theory, thicker soap has more soap and less water, so it is better.  Cheap soap manufacturers add cheap chemical thickeners to make poor soap seem like high quality soap.  At this point, I don't think it means much.