Just to fix that last thing:
If the Earth is a spheroid, gravity exists because all objects with mass attract all other objects.
If the Earth is flat, UA exists because apparently everything in the universe has exactly the same amount of force being applied to it (the stars, the moon, the planets, the Sun, and the Earth) and thus accelerate at the same rate, except for the objects ON Earth.
If I'm grasping UA wrong, then please elaborate, because the FAQ's didn't help me in that respect.