Her background is as murky as her brother's!!!
She can be an American citizen, in the eyes of US Law, if not Indonesian, because she was born outside the US of a US Citizen parent and an alien parent, and by then Stanley Ann was elibible to pass US citizenship on to her child. She was not when Barry was born, if he was born outside the US. But it's not citizenship that is at issue, if born in the US Barry is a citizen, and telling the Indonesian authorities otherwise doesn't change that. However since his father was not a citizen, ever, unless he's lying about who that was, he cannot be a Natural Born Citizen regardless of where he was born.