Both had plenty of experience since they took their first flight lesson ever. I was taught from an early age that when u level off from a decent, u have to push the power back up or you will stall. Ice, no ice, ifr or vfr, doesnt make a difference. I don't see what operation experience or adverse weather has to do with pushing up the throttles. That's basic airmanship in my book.
He didn't even push the throttles to the detent (when he could have gone way past the detent for max rated power) after the stick shaker.