GUEST, it's not that unusual for the banks of a river, located in a town or region, to be referred to as "the banks of the town or region of so-and-so." In balladry, the "Bonnie Banks o Fordie" is an example, Fordie being a region near Dunkeld that had a pretty burn running through it, not a river named the Fordie. Thus, it is the banks of Fordie, not the banks of the Fordie.

A modern example of this usage would be this site, which has a photo caption stating "Picture of fisherman and Atlantic Salmon statues displayed along the banks of the town of Campbellton, New Brunswick in Canada."

Also, "banks" was used to refer to earthworks, levees, dykes or sea walls used to shore up a town from encroachment by seas or river surges. An example would be the charter for the town of Poole, dated November 24, 1667, which authorizes taxation "for and towards the necessary reparations of the bridges, walls, and banks of the town and county aforesaid...." Since Dundee does have a sea wall, and is known to be on an estuary, it's not hard to imagine an imaginative writer referring to "banks."

This is, or course, only one theory, and it may be just as you say: a fictional river called the Dundee, which can join "Scarlet Town" and other fine fictional ballad locales in our mythic geography.