I had this whine too. They replaced the P/S reservoir, no more whine. There was a tsb for this on the infiniti side. I imagine there's one for the 370z too.
http://www.infinitig37.com/TSB/ITB12-035.pdf
Now it is possible your noise was indeed due to a bad p/s pump. Mine sounded like a supercharger whine. It was present mostly after the car was warmed up, especially in ambient temps over 60F. Just turning the wheel one way or the other while stationary would cause the whine.