In the Pressure and Impact chapter the Impact Movements video talks about pushing down with the arms through impact and in the Speed and Strength chapter this is enhanced as a point of additional power because the pushdown can actually add a little bit of forward speed to impact.
I have not heard of it being called a punch down but more just a push down. One thing I would be concerned with is if we “punch down” we could get too active with the arms and cause the body to stall out losing that safety of the club face. A lot of this could be a feel thing as well, in which each person would feel the move in their own unique way while at the same time executing the move very similarly. Personally, I like to feel a push down as part of building pressure and acceleration through the strike. If I don’t have that acceleration through the strike, then I dump all my pressure into the ball and end up with a weak slice or a pull hook as I lose control of the club face.