There's another story, probably apocryphal, about how the term is actually a misspelling of a term from an early rock and roll band which had only one mic, but two vocalists. Trouble was, one of the singers was Russian, and when he wanted to know who was going to take the next vocal part, he'd ask: "My sing? Or your sing?" And 'my sing' eventually got bastardized into its present form... Well, that's what I heard.