I haven't had a chance to get that video lesson downloaded yet. But I think that's right.
With the SA swing, the arms are for practical purposes in sync with the body. If the body turns away from the line too much/ too soon, the arms are going left. That's what I've been getting while trying to get more turn.
It's easy to feel the contrast in my Stricker swing, where the body pulls the arms through later in the turn.