To understand the sunrise/sunset according to this model take a piece of paper and draw a big circle (the flat earth). Draw another circle inside this one from the same central point but half the diameter. This is the equator. The northern hemisphere is the smaller circle and the central point is the North Pole. The outside of this circle (the other side of the equator) is the Southern Hemisphere and (as you have no doubt noticed by now) is not a point, rather it is the circumference of the circle. It is a rugged icy mountain range. This is what we refer to South Pole. etc more here:
The point is that you can explain some phenomena using a "flat-earth" model.
I couldn't go through the scientific explanation but that is what I understand.
This only shows the wisdom in the explanations used. So it is true in one sense because the model describes phenomena. Just like we can fulfill the phenomena of looking at a big round sphere and saying the earth is round.