Her answer off the top of her head was . . .

the only thing i can think is ps/ss hagrid telling harry his name was down since he was born.

That sounds right to me. But I do think JKR talks about magic manifesting later in one of her interviews so I think you could argue there is always an exception-or what about Neville? His family kept doing stuff to him to see if his magic would kick in. *rolls eyes*