Is it not enough to self-identify as Jewish to be Jewish?
To be officially (rabbinically Jewish), your mother must have been rabbinically Jewish. And so on.
I'm not sure but I think the issue with JC, is that his dad (AC) was jewish but his mum wasn't.
So he has jewish heritage but he isn't officially Jewish. (Why is it such a struggle to persuade the iPhone to capitalise properly?)
That's the short answer.