Look at 1:13 into the video. Both players have their wrists folded. And then a few seconds later the coach does it again to emphasize don't fold the wrist. It looks to me like he is only addressing the folding of the wrist. I don't think he is addressing wrist cocking in that sequence, but perhaps the OP can definitively clarify.

At 45 seconds when the coach is demonstrating brushing technique you can see some wrist movement, but it is definitely not a folding action. 

yes OP please elaborate.  Ieyasu, thanks.  I misused the terms.  When I usually say cocking , I mean it (wrongly) on an off axis way - which is what you (and the OP?) mean by folding.  Then how does one fold the forearm?

The translation is confusing. I THINK what he means by folding the forearm is the angle that the forearm and upper arm make is reduced when swinging forward. In other words, the entire arm although not exactly straight, is closer to 180 degrees than 90 degrees at the end of the student's backswing (against backspin balls), but when swinging forward that angle reduces, ie., becomes closer to 90 degrees. In order to do that one needs to move/snap/accelerate the forearm, so that the angle at the elbow narrows. That is my guess as to what folding the forearm means. Sorry.... hard to describe in words.

If you watch the vid where folding the forearm is discussed, the coach nods his head in approval as the student's arm bends when swinging forward, instead of keeping his arm straight.

Is the coach a guy? I thought it was a girl. Am I the only one that thinks that? Sorry if I'm wrong.

By folding the arm, I'm pretty sure he means to go from a straighten arm to a bent one.

BTW, The coach is a girl. 

That does not make sense to me.  Could you explain further.  Is it turn like in turn a car or more like turn a doorknob or something else?  Always interested in different ways to explain stuff to students.

Mark

I knew the coach was a girl even though her hair is very short.  By not folding the wrist, does the coach mean not to use the wrist at all or not to fold it (too early)?

I took it to mean to make the wrist component as small as possible, the main action was the forehand. My question is whether this is just a beginning technique and LATER after you learn this you add wrist snapping, or not?

Sometimes we call it "shaping" the ball where I was born.  The idea is that your racket should rapidly go on a trajectory that forms a curve around the ball as opposed to hitting into it. It can do both with thick contact b it the focus should be on the racket path not on trying to hit ball with flat contact.  Brushing focuses too much on the quality of the contact while turning in my opinion focuses on what the racket path should be trying to do as well as the contact.

 above clearly explains the wrist usage

@vanjr Using the wrist isn't wrong, it's just wrong if you drop the wrist like what the coach showed in the OP's video. The link tom added above demonstrates it nicely! I definitely can't do that though hehe.