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That's how I first read it too.I hope he comes back to clarify . . . I was reading "inverted" as lying on one's back, which is where I have seen the buoyancy difference.
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I'd guessed that is was the reduction in the total surface area presented (relative to gravity)... but I really don't know if this is correct.
You guessed correct.
When you achieve neutral buoyancy in horizontal trim, you have a lot more surface area presented to the water column than when you go vertical; inverted or otherwise.
When you achieve neutral buoyancy in vertical trim and go horizontal, you will find yourself slightly positively buoyant.