I have found that a lot of white women do this in the presence of black women, this sort of mild passive/aggressive thing, like they feel some sort of way about being around black women and need to prop themselves up higher, but without actually coming out and saying so.
Don’t forget, the Williams sisters have had to fight against classism from people like Campion too, and that also might be a factor. She could have said that against any women in the room, but she chose them, and tried to diminish their accomplishments by saying that.
I also think she was probably unconscious of how she sounded as well. I’ve met enough white women who did this around me and my friends, that in most cases I don’t even think they know they were doing it, but we could feel that they felt something by being around us. They felt a neurotic need to lift themselves up at our expense.