With the Greek living US parent if they had never lived in the US the kids might not be citizens. I don't know the details but I read once that if you are born overseas of US parents and never live in the US your children are not US citizens. You have US citizenship if you want but it doesn't pass down unless you actually claim it.
There is another bit of the law that might apply to Clark. I can't find it, read an article about the only time it has ever been applied and can't find it. A child found young enough in the US who isn't shown to not be a citizen by a given age is even if latter evidence shows that they weren't. Maybe someone better then I as researching US law can find it.
