Correct. The lighter the parts of the map are, the more specular is being used. Solid white is like pure gloss, while solid black is a very dull look.

EDIT:
To darken it -> open it up in photoshop, then select the image>adjust>brightness and contrast option. Drag the slider down to darken it. Or, if you don't have any software for image editing, just make a black square in Paint and save it over the spec map. That'll remove all specular used.