Why would you need to carve the turn if you have the bumps? Don' they come "towards you" where you can push off from?
When you ski the technical line, there is no mogul coming towards you on the backside turn. It is usually a fall away smooth slope until you reach the bottom of the rut. The skier also needs to carve a turn into the mogul face as it is up to the skier to engage the mogul face squarely, it doesn't happen automatically, the skier needs to navigate the steep natural mogul terrain with highly developed turning skills just like a racer needs to navigate around the gates on groomed intermediate terrain.
I agree with tdk6 that the term "push" is doesn't quite equate to the jarring impact of slamming into the side of a mogul with your feet while carrying speed. The terrain needs to be absorbed and speed control must be gained simultaneously somehow. I'd say push should be replaced with pound.