You do raise an interesting point here. However, I'd venture to say that the crossover plays both ways. A basketball player might struggle during a long shift, or be rudimentary at skating and stick skills, but the hockey player's in the same boat. He may be able to dribble, pass, and shoot, but only at the fundamental level as well. Hejduk isn't going to be able to drive to the basket on NBA players any better than Chris Paul is going to be able to crash the net against NHL players.
In keeping with my original cognitive and physical combo point from my previous post, look at that D. Rose video. He's making all the calculations I mentioned, getting airborne, then completely changing course and moving the ball in a different direction mid-flight. The amount of agility, speed, and plain ol' movement involved in one shooting play of his reads like a physiological scientist's wet dream. In hockey, a little bit of stickhandling and a feint before a shot is about as multifaceted as it gets during a single scoring attempt.