Let's say, on the same day, the President is killed by a living pretzel named Edgar. While the Vice President is being motorcaded to the SEKRET BUNKER OF HAPPEENESS, his limo is crashed into by an old lady. The Vice President dies (but the old lady lives, her cancer miraculously cured
somehow...).
The Speaker of the House is an immigrant. Is he sworn in, even though he was not born in the US?
(and if the answer is no, pretend that by some magical twist of fate every single other person in the line of succession is an immigrant)