In some of his videos his head does move a bit, so he is probably not suggesting we freeze like a statue. Most of the movement comes from one place, the left arm. Everybody is different, but you can't argue with the results he gets. I've watched some of his recent videos and there is no way I will ever be that good.
Interestingly, Max De Aloe, whose book I've been using, suggests the exact opposite method. He suggests moving the head and keeping the harp still. However, when you watch him, he does move the harp some.
It seems that each of these top notch players agree on one thing: most of the movement should come from one place. At least when first learning. Now, perhaps they are saying this because they are aiming this instruction at beginners. After all, if you are talking about how to hold and move the instrument, you are talking about a very basic first step. Perhaps at that point it is best to not confuse the beginner with combinations of movements. When I took golf lessons my instructor did the same thing. He had me learning isolated movements and then combining them later.