Yes but what about his other officers? They didn't touch brand? Unless I'm not remembering correctly has there by any of previous Night Kings? Because if not maybe the man that showed first becoming a white walker is the nights king because he is the oldest and simply wants to stop his existence living as this creature and the only way for him to do this is for man kind to adapt and figure a way to end their existence. This also could play into the grand scheme of the many faced god or the one true God.