When you create a superflat world, no matter what Y coordinate the ground is at, lighting changes as if you are in a cave a certain distance above the ground.

This same thing happened on three different superflats I created, each with a different ground level (y=-61, y=-19, y=5). 

I have found that each time you reload the world, the area previously in darkness is lit properly, with the lighting error now occurring higher up.