According to wikipedia: "In English usage, Scandinavia is sometimes used in an extended sense that is synonymous with the Nordic countries." I myself used the term as a sub-category, as all Scandanavian countries are also Nordic. The customs questions indicated that everyone was stopped because of the high tax on alcohol in Denmark. Other Scandanavian countries have simliar taxes, but I don't know if the same is true of Finland.

I don't really think there is much doubt that Denmark is part of Scandanavia. At various times in history Denmark consisted not only of Jutland and the nearby islands, but part of what is now southern Sweden and at other times much of what is now Norway. On pure geographical grounds (as you indicated) the argument could be made, but I'm not sure many Danes would agree to a re-classification.