Turns out that in shifting outside, I was shifting further forward than he approves (out onto my front foot for a left hook) -- had very little to do with turning the hips, but rather that thing about keeping the weight BACK again.

My hips have really crappy flexibility (my knees too) so that is always an issue for me to go low and still keep my form upright (and therefore back). My head and shoulders tend to go forward as I squat, even though I work on this every day.

Mostly, it was just that he isn't always very clear about what he REALLY MEANS, even though he is generally a really good coach.