I'm not sure whether or not Disney was going exactly by the fairytale, but it seems likely, as Disney does research their fairytales extensively. In the original tale, one of the sisters is not as mean as the other. The oldest sister is the meanest, but it is the youngest, who is not so mean, that calls Cinderella "Cinderella." It seems that Anastasia is this younger sister, as she is shown to be not as mean as her mother and sister.
Reference: Cinderella and Other Stories from "The Blue Fairy Book."