I wouldn't be too sure about Jesse James and Billy the Kid. The key is that they were both born in the U.S. It's well established that young children are far more influenced by the accents of their childhood friends and schoolmates than of their own parents!

As an example, I know a man whose parents both immigrated to NYC from Scotland when he was about six. Both his parents had unmistakable "burrs." When I met him, in our twenties, all trace of his Scottish accent had permanently disappeared.

The cutoff age seems usually to be something like seven. Henry Kissinger's family emigrated when he was fifteen, and he's never lost his German accent. Schwarzenegger came as an adult. Mel Gibson went to Australia at twelve. He could do an Aussie accent in "Gallipoli," but obviously he never lost his everyday American accent either.

I suppose everyone knows by now that languages and accents have nothing to with one's genes or (except through the influence of those around one) geographical location....