No Vaux, the game engine argument wont work on this one. See in real time lets say, 2 people on opposite sides of the planet can in real time look at their sky with this app, see with their eyes in the sky the stars, then look at the screen and see it matches the sky. Then in real time, slew slowly down towards the ground. And if both were video taped while doing this, you would see that the sky they see through the planet will match the skys of the other person. Showing that the night sky of the other person must be on the other side of the ground you are standing on.
Now sure, if you only have two people that can be simulated, but 10? 10,000? One million? At what point do you have to say, to maintain this "conspiracy" is becoming exponentially harder and harder, which is the easier explanation... Flat or Round?