This is an argument that's been waged for ages with no conclusive result. It all comes down to semantics. Define "push". Some consider it late, some early, some not at all. Some say it's a "pull". I don't buy that one either.
The problem with this term "push" is that some kid out there takes it and opens up the hips and shoulder to face the target while the weight is still back near the rubber and then pushes that way, thinking this is the source of power. There's also the danger of getting the upper body out too early (the most common definition of "rushing" I've seen).
I try to avoid the term as much as possible. Instead, I like to describe it as a "drive" sideways. On another board, a very knowledgeable poster used the term "rotational push" into landing. I like that one. Dick Mills uses the term "lunge". That's not bad either.
It's all about how to get a player to do what he needs to do. "Push" just isn't a very good term to use. It has too many issues. "Lunging" or "driving" sideways with a "rotational push" into landing is a far more productive mental cue than "push".
Who says so? Check out the pros. The back foot is nearly completely turned over onto it's laces by footplant. How can you push in this situation? I can't buy the push after landing thought. The actions of the pros just don't support this contention.