Haha wow you guys have really gone off on a tangent of miscommunication! I have a feeling you both know exactly how it works :P
Let me lay the smack down:
*** BUOYANCY IS CAUSED BY A PRESSURE GRADIENT APPLIED TO AN OBJECT ***
A pressure gradient is usually caused by density of the surrounding fluid and a gravitational field. On Earth, the pressure gradient is only a function of the fluid's density. So it's good enough to say the buoyancy force on an object is only a function of the surrounding fluid's density (and the volume of the object).
In the above I'm ignoring the self weight of the object, which of course needs to be added to convert buoyancy force into total, measurable force. Here we have a semantic issue. Paul, your two-spheres-underwater example assumes it's the total force, but I think it's more correct to ignore the object's weight (and density) when defining buoyancy force. Either way, it doesn't change reality when we apply whatever definitions we each use.
In the case of a ball of water on the ISS, you raise an interesting point Paul. The water would have its own local gravity field, which would cause a pressure gradient inside it. That would cause boyancy of a ping-pong ball. Even tho this force would be amazingly tiny, what would stop it? The viscous friction of water approaches zero as speed goes to zero. So I'd think the ping-pong ball would actually move to the surface. But it could be extremely slow, and maybe other tiny forces like photons hitting it, or the microgravity of Earth would overwhelm buoyancy.