I'm quite sure to not have fully understood your question, so before giving you some suggestions I would like to punctualize one aspect (as I have seen you are interested in compositing layers):
No transparency is involved in this scene, dark grey color of the plane/cube in shadow comes first of all from interaction of the plane/cube (diffuse white) with the world background light (which is colored dark grey). All the visible surfaces will produce a white alpha channel area.
You can remove the world influence on the scene by lowering the Background strenght to 0 or even completely remove the shader.
You can set the Max number of bounces of light allowed for each light source in the Lamp panel in the Object Data tab.
You could also tweak the "global" light path bounces, but you'll not have the precise control that the "per lamp" option allows.
By seeing your third edits I would suggest the following (more general) instructions:
- Switch all lights off (Background too), except the light source you would like to isolate. All the light present in the scene is it contribution
- Set the amount of bounces allowed for the light source (per lamp, or
globally if you are using an emission shader as a per object option
is not currently (2.75a) available)