That is truly laughable. If the sun is above the disc, there will be some level of daylight across the surface. True darkness won't happen until the sun is below the earth's surface.

Another question would be, what light is reflecting off the surface of the moon if the sun is on the other side of the disc?

You still didn't answer any of my questions. I was quite honest in asking them. Under that model, the constellations would be the same no matter where you stood on the planet. And yet they're not. Answer that.