Tou were right in the first place - "Twin Sisters" was and still is a Canadian tune (Newfoundland actually), collected there by Maud Karpeles. She "introduced" the tune to the Upton Stick Dance. Now almost everybody thinks the tune is called Upton Stick.
But the old Upton side danced it to Brighton Camp (and Flowers of Edinburgh and similar tunes), as do traditional Border sides to this day. It gives a totally different feel to the dance, emphasising the stately, ritual elements inherent in the dance rather than being just a frenzied scurrying around to a "foreign" melody completely unrelated to either the town or the dance, but a good excuse to let out some Amerindian war whoops.