She's actually NOT Jewish. To be Jewish her mother must be Jewish. Her mother is Catholic.
I don't think most modern Jews accept that (except when they don't want to consider someone they're ashamed of to be Jewish, like Dr. Laura). I've met any number of Jews in NY and LA, the liberal modern sort, who regard themselves as Jewish or half-Jewish irrespective of which parent is Jewish.
BTW, what reason for this rule? A talk radio caller, after discovering her own Jewish roots, claimed to have studied the issue. She said the rule exists because in ancient and medieval times, rape was common. Tribes and warriors would routinely raid each others' villages. So because rape was so common, it was often impossible to tell who the father was, but if you had a Jewish mother, you were certainly at least part Jewish.
Don't know if it's true, but it's an interesting theory.