You are right. fregus leaves it at "ambient light" and calls it a day, but ambient light is just an empirical construct, not grounded in physics. In reality, light bounces around, and areas will appear darker the more the light paths otherwise converging on them are blocked by occluders.
I think "overlapping shadows get darker" is just not a very intuitive way to think about it because it disregards the stuff that actually matters, which is the light sources and how the scene may block their light paths.
For early games that could not afford advanced methods of global illumination, making overlapping shadows get darker seems like a reasonable, though not necessarily correct, way of faking it.
And the other thing ignored in these comments is perception. For the case of the two businessmen looking at their shadows under a bridge, it is easy to show with a diagram that some areas of overlapping shadows are, in fact, darker. But in such a poorly lit scene, people are likely to conclude that there is no difference, which isn't to say that there isn't one but, rather, that they don't perceive one.
