Well, people should realize that major airports are usually not located in the town they "think" they're flying to/from. A few days ago I flew from home to Paris and back. In real terms I flew to Orly and from Roissy, both of which are towns in their own right. In contrast my home airport is within the limits of the city of Heraklion, but since there is no train there is no confusion...
Keep in mind that Rome as a smaller, second international airport, Ciampino, which has no train connection, though.