Hunter / gatherer society was organized in a form in which they had not settled, as probably they started doing during the Mesolithic and then the Neolithic periods in which humans discovered the agriculture and with this, they started to develop more complex forms of social organization to finally arrive to specialized roles and labor division.
As a conclusion, social roles, coming from specialization of labor and its division according to the group´s needs came after the hunting / gathering behavior, so this statement might not be true.