I wouldn't be surprised if the boss has a Western connection, but the Nanatsu no ko song is a dead giveaway the boss spent a good deal of time in/was raised in Japan. Nobody outside of Japan is familiar with that tune. All known confirmed facts about the boss are listed on the wiki page. If it's not there, it's probably a rumor. The boss's nationality has not been confirmed at this point.
To be fair, the FBI may only be involved with the BO because the BO extended its reach from Japan to the United States (and possibly other countries like England), and caused criminal trouble that attracted the domestic agency. The FBI may not have realized right away they were dealing with an international mafia-like organization. Also the FBI actually has overseas offices attached to embassies, including one in Japan. They help with crimes that cross national boundaries.