Hi Paul &Dot
Yes, it's not difficult to sway my hips and keep my shoulders horizontal. But this isn't what i try to do when i'm dancing. All the dancers i've watched show the shoulders and upper torso nicely 'aligned', as i tried to describe. For example (but by no means exclusively) Jonathan's slow waltz natural turn on this site.
On another point which was made by cdroge, it's true that with a movement like slow waltz natural turn, the strong swing gives a strong 'upward' feel, and this feeds into the sway. But there would be figures with much less swing (example, step 4 of a weave in foxtrot where the man steps back in CBMP and there is a sway to the left) and in an example like this, it's much easier for the man to collapse the left side (in this example).
I think it's very good advice to think of both sides being stretched and to think 'up' when swaying. This works in all cases(that's a dangerous thing to say!!)