I think you're right; the diver who is perfectly horizontal cannot compensate for not being neutral by swimming up or down. But that also means that the horizontal diver will instantly be AWARE of not being neutral, whereas the head-up diver can swim around negative and not know it, unless he tries to stop.
Trim and buoyancy are intertwined -- UNLESS you are motionless.
Trim and buoyancy are intertwined -- UNLESS you are motionless.