What happens:
After the first tab of your nested (child) tabview, the [[/tab]] tag ends the tab of the parent tabview, NOT the child tabview. So, the rest of the tabs become switched (the parent tabs move into the nested tabview, and the child tags move to the parent tabview).
It's hard to tell when there are an equal number of tabs, i.e. as this author has done - "A, B, C" and "1, 2, 3" - but note that the tabs go "A, 2, 3" in the parent tabview and "1, B, C" in the nested tabview.