If I understand correctly, headspacing is enforced by the relationship between the barrel and the bolt assembly and has nothing to do with the upper. Am I understanding correctly?

The reason I ask is because I'm thinking about replacing my upper. I think I would be okay with swapping my barrel from the old one to the new one, but if there is the chance of headspacing changing, I would probably want a qualified gunsmith to check it for me.

The headspace cannot and will not change with a new upper.  Do it your self.  Save your cash.

As you note yourself the headspace is determined purely by the mechanical relationship between the bolt and the barrel.  

On the M16 system the locking lugs are a permanent part of the barrel and wherever the barrel goes, they go.  The receiver just holds the parts steady and doesn't figure at all into the headspace question.

-- Chuck

Thanks, that's what I thought. :)