An Old Sports Illustrated article I saw many years ago, talked about something like that. Janet Lynn's coach accused Julie Lynn Holmes of stealing Janet's hand positions.
Also, some coaches are like Mike Brady in the Brady Bunch Movie. I'm talking about the part where he keeps designing buildings for companies that look exactly like the Brady home. The coaches have a signature style, and put each different skater in the same mold. You could almost always tell who was a Fassi girl, or a Heiss Jenkins girl.