This is correct for some of the punches but not for all. We have both circular and linear punches. With the circular punches it's going to be impossible to "keep" the weight behind the punch. So in that light you are correct
But our linear strikes are almost the same concept. With linear strikes we still throw our weight into our punch but the only way to do this is to make sure that the weight is BEHIND the punch. Here's the videos that you referenced. The punch at 0:48 would be considered a shuffle in Jow Ga. We say the same thing, use our feet to get to our target. However, stepping for Jow Ga is like walking, where the rear foot goes to the front in order to advance. Stepping in Jow Ga can also mean that the front leg pulls the body forward.
With shuffle steps, one leg always stays in front while the rear leg pushes forward to move the body forward. The only thing required is to move forward is to lift the front foot up and to push with the rear. The biggest difference that I see that after the front foot lands, he slides the rear foot up a little closer. It's like a hidden advance or a reloading of a push. This is common with fighters who have the weight on their back legs.
Fighters who fight 50/50 (which is really difficult) are ready to push forward or backwards without shifting weight to one leg or the other. In the video he mentions that the rear foot "catches up." In Jow Ga this is common with the circular punches, with the linear punches it just depends on the technique that will follow the punch.
This is a video I took of me last Sunday. My legs almost stay the same distance apart but I'm able to move with no problem. In the video, I'm going slow and only focusing on technique so I can see where I need to fine tune and correct parts of my form. If I go at the speed I'm supposed to practice in then the camera would blur and I wouldn't be able to tell where I'm screwing up.
Over all I think we are talking about the same thing. I just think we had 2 different perceptions of what a "step" is and that was throwing us off.