I believe the initial motion of the hips is supposed to initiated by the intention of moving the lagged club with the hands-"hands/lag-controlled pivot".
You are absolutely right.
But Monitoring (5-0) the Pivot (Pivot Controlled Hands) during learning (3-D) is a good way to incorporate the above into one's swing. Once the desired Pivot components are mastered, you go back to the Hands Controlled Pivot procedure.