You and your group are free to run your table however you choose. I would not choose to play at it. To me classes are sets of mechanical abilities. The fluff given there is the default to help people along with their character concept. There is nothing wrong with using the barbarian mechanics to represent a noble house's secret martial training, for example, provided such a thing can fit into the world. In a world with people who can speak fire into existence, the gods may well walk down the street to the corner pup and with flying talking lizards that can breathe fire; I would argue that there is a room for many, many tamer things.