(edit... I see Jonnythan was posting while I was typing... so this is a little redundant)
Buoyancy is strictly a function of water displaced and weight.
However...
"Neutral buoyancy" is much like balancing a stick vertically on your finger... you have to keep moving your finger around slightly as the stick tries to fall off.
Likewise, if you are perfectly neutrally buoyant and get displaced upward, the gas in your BC & the bubbles in your wetsuit will start to expand and you'll just continue to go up. If you're neutral and get displaced downward the gas in your BC and the bubbles in your wetsuit will be compressed and you'll continue downward...
So, you have to do something to counter this instability, and that is timed breathing. If you're neutral and inhale, you'll get positive and start up - so you have to exhale to counter it. But since you're moving up, you have to exhale more than you inhaled to stop it; you have to get a little negative to counter the momentum. If you just stop breathing as you stop going up... you'll go down. So you have to start inhaling before you even start going back down to get neutral again... and so on.
Now, a change in position is going to cause some vertical movement somewhere - if going from horizontal to vertical then probably upward with your lungs and BC, so you can expect to start up and need to exhale to stop it. So while a change in body position itself won't change your buoyancy, a move upward of just a little bit with the BC or your lungs will...
Make sense?
Rick