Tried to copy and paste from the article. It did not work.
Under legs it says to keep knees bent. Toward the bottom it talks about raising and lowering the heels.
COULD this be don keeping the head level? Sure.
IMHO trying to keep the head level while doing this would not be natural and require unneeded effort. The issue of the head raising and lowering as a byproduct of the methodology is not mentioned.
So why the up and down movement then? Am I missing something? Again, you can flex your knees and raise you back heel without moving your head up and down.