Here is a link to a thread with more information about different types of jigs. Fionn, your informant is correct: single jigs go "humpty dumpty" while double jigs go "jiggity jiggity". Both of them are written in 6/8, but the difference in rhythm could certainly affect which dances would go well to which kind of tune.
By the way, just because there's no hard-shoe version of a slip jig dance doesn't mean that there are no dancers with hard soled shoes who dance to them. Such as me! Step shuffle, hop shuffle, hop shuffle.