Does a counterexample exist? Could he have been born in a different year? Justin Bieber was born in 1994.
Argh, I blame my former reply on it being Friday night. If the date of his birth happened to be close to the very end or very beginning of 1994, then the pregnancy could have been extended or his birth made premature due to natural complications, changing the year to either 1995 or 1993.
Since his conception under actual "test-tube" circumstances would probably be even more unlikely, the other possibility is Bieber's early embryonic stage being removed, frozen for the necessary time, and then implanted back into his mother or another host to change the year he was born. But not much less fantastic.