In short, CG images are created backwards. In real life light is coming from a source, bouncing off something and then into a camera...
In CG, a line is drawn from the camera until it hits an object surface, That surface is examined to see which way it is facing. If it is facing a "light" (really just a point in XYZ space) it is drawn brighter, if it is facing away it is drawn darker. So there's nothing really "bright" about the "light" itself. It's really just a marker that the computer uses to calculate if the object should be light or dark.
In A:M, when a light is given "width" other than 0, it isn't like a large sphere that is emitting light outward. The position of the light is jittered randomly around that space. It's possible that if a light width were larger than an object at the center some of the jitters might result in a surface being illuminated.