Well, the Romans did lived on the Middle Ages, in the form of the Byzantine Empire, Based on Byzantium (later Constantinople, then Byzantium again, then Istambul from the turkish takeover to this day) direct successor of the Eastern Roman Empire. In fact, the fall of the Byzantines marks the end of the Middle Ages.
Anyway, this is a game, and as such, the more it advances in time, the more it have to deal with "what if" scenarios, for the sake of fun. Imagine reaching a new age and a pop-up appearing saying that your current Civ is no more and you must choose one that truly lived on that era?