Try this completely different thought experiment...
Draw a large circle on the ground, 10 or 15 feet across. This is going to be the orbit of the 'moon'.
Get a friend and stand him in the centre. He is going to be the 'earth'.
Stand on the circle, facing anticlockwise, and start walking on the line of the circle. Your friend is allowed to turn round and round if he wants to, at any speed he likes, which is the earth's rotation (and completely irrelevant, as you will see).
After one complete circuit, you will also have turned round once, just like the moon does every 28 days. Ask your friend if he could ever see your right side and shoulder! No, all he could ever see was your left side and shoulder.