Before that I just need to clarify that your claim is points on the earth will receive on average six hours of daylight as predicted by a circle of sun half the radius of the earth?
Are you saying these are incorrect numbers for these positions or that the sampled cities cannot be generalised across the earth?
It doesn't matter, it's not every point on the earth, it is any point. If at any single point on any day if you get twelve hours of sunlight under the assumption that the sun did not slowdown as it passes you, you can tell one of two things, the perimeter of sun's circle of light has passed one of the poles, or the sun does not cast light in a circle of radius half that of the earth's.
I could show the geometry if that is in question?