In this case, I think you BOTH were correct, but weren't speaking exactly the "language." If you arrive early and depart late, four nights = five days - - right?
So, to be more clear, Disney typically only uses the term "Nights" in their offers. The current offer (click
HERE for details -- it is a pretty exciting offer!) is "buy four NIGHTS, and receive three NIGHTS free."
By the way, if you ever are confused by the information that a Cast Member provides you on a phone, please don't hesitate to call back and ask another Cast Member to help clarify the details. I often do this myself. Since there is SO much information the Cast Members need to learn, it's only natural that they give you some "Goofy" responses once in a while. ;-)