You people are assuming the moon is a sphere. You see the same face because it's not a sphere at all. It moves over the Earth from one side to the other, so people on one side of the Earth will see it face up and as it passes over to the other side, people from that side will see it face down.
It's like shining a batman torch over your ceiling. You start off seeing the bat the right side up and as you move the beam over your head and behind you, making sure you don't twist the torch, you will see the bat upside down.
So what does that tell us?
It tells us that what we are seeing is a reflection of light moving, not a physical body in the sky.