"But... the center of gravity!" I can hear you cry.  Yes, in order for the character to be balanced, the center of gravity must be over the zone of support.  But that's not the only requirement.  The other requirement for Static Balance is that the legs must be bearing their proper amounts of weight.

Don't believe me?  Again, you'll need to stand up.  Try pushing down with your right foot, but not moving your pelvis.  Can't do it, can you?  Either you move to the left because the leg pushing down throws off your static balance, OR you move to the right because your body anticipates the need to apply pressure to the right leg, and unconsciously shifts your weight.  Either way, however, you cannot push down on your right leg without shifting your pelvis.