the apple has greater density than air, which is why it fell to the ground. It's not gravity, it's density.
Engineering student here who has taken physics up to the electromagnetism level - you still need gravity for that explanation to make any sense. The force that drives buoyancy is gravity. See the following diagram:
The reason why things are pushed up in a liquid is because pressure increases as you go down. When you displace water with some object, the bottom of the object is being pressed upwards harder than the top of the object is being pressed down, hence there's a net upward force.
If you pretend gravity doesn't exist, then nothing happens. Being 'dense' doesn't cause forces, it just means you have more resistance to force per a unit volume. If you were to go into space (or a vomit-comet if you choose to assume space isn't real), you'll find that a bucket full of water with a steel ball in it will exert no bouyant force because there's no difference in pressure along the column of liquid.
