I quickly set up a similar scene to determine what is happening with the renders.  My first observation is that the shaders on the figure and clothing are not optimized for Superfly and are responding to the 'Sun' light source.  That is why the figure darkens as the light intensity value is decreased.  My second observation is that the shadow on the shadow-catching ground plane is responding to HDRI illumination, not the 'Sun' light source.  That explains why varying the 'sun' intensity has no effect on the shadow density.  

Check if the 'sun' light source has Shadows unchecked in the Properties Tab.  My suspicion is that it is unchecked, otherwise, you should have 2 shadows on the ground plane.  The solution to lighten the shadow is to place a low intensity, non-shadow area light or spotlight pointing toward the shadow behind the figure.  This is a hack but it will make the render more acceptable.