I think the hypothesis has merit, and also that the word "matrilineal" doesn't quite seem to fit. Maybe "gynocentric" would be more appropriate?
But whatever it's called the author's description of the cultural dynamics seems accurate. However, I don't think this dates back just to World War II. Having read southern literature from the mid-to-late 1800s, I think southern culture at least has matched that description since at least then. Perhaps it was a legacy of matrilineal or matriarchal African cultures, as many upper class women in the southern states were raised by slaves; but perhaps it was also accelerated by the killing of about one fourth of the adult male population, and the wounding or maiming of about two thirds of those who survived, during the war between the states, which of course forced the southern states to rely on its women because so many of its men were dead or disabled.