Wouldn't Jesus more correctly be a Galilean? If I recall correctly, the word Pontius Pilatus used when he said of Jesus "king of the Jews", was "Ioudaioi". And at the time "Ioudaioi" was used to refer to all of the Jews, not just the Kingdom of Judea.

This is like proclaiming that some Italian is now the king of all of Italy, Spain, France, and Greece.

Edit: basically, Pontius used Ioudaioi when proclaiming Jesus king of the Jews, as an insult.