Little physics problem

[Joe Horn]

Doesn't the answer depend on whether the object is airtight (like a glass sphere or submarine) or open to the air (like normal boats)?

Here is my guess: (1) Unless I'm mistaken, an open-air object's buoyancy is determined solely by its mass and the mass of the water it displaces (thank you Archimedes). The surrounding air pressure has nothing to do with it. Therefore lowering the air pressure by bringing the object to a higher altitude would not change its buoyancy.

(2) On the other hand, a totally enclosed object like a glass sphere full of air would keep the same mass but would also physically EXPAND (slightly) when raised to a higher altitude (the way balloons expand as they rise in the atmosphere), thus requiring it to displace (slightly) more water to "just float". The effect would therefore be that the object would float (slightly) higher in the water at 3km altitude than at sea level.

Disclaimer: Stop laughing, I'm no physicist, I'm just guessing here, because it's fun to perform thought experiments like this.