A Druze toddler from Israel, "O’Neal Mahmoud," was recently discovered to speak English with a decidedly English accent, despite claims that he was never exposed to this language. In fact, they say he speaks English much better than Arabic, the language of his parents. They don't show him saying much on the one video I found that shows him speaking, but he definitely sounds like a native English speaker to me. The Israeli newscast also says he only speaks Arabic with a heavy English accent, which of course I can't confirm.
It must be said that speaking a foreign language without an accent is something young children can do exceptionally well, and it wouldn't take much time or exposure for them to learn it. On the other hand, if an adult can suddenly speak a foreign language they've never studied before, that would be pretty amazing! Here are some less recent examples of older people who have suddenly developed an ability to speak a foreign language fluently: Matej Kus, and this girl from Croatia. I've got more stories like this from my other blog if you're interested.