From the official website
Q: Who is eligible to play in the World Baseball Classic?
A: The following criteria will govern player eligibility in the World Baseball Classic:
The player is a citizen of the nation the team represents, as evidenced by a valid passport the player holds as of January 15, 2006; or
The player is a permanent legal resident of the nation or territory the team represents, as evidenced by documentation satisfactory to World Baseball Classic Inc. and the IBAF; or
The player was born in the nation or territory the team represents, as evidenced by a birth certificate or its equivalent; or
The player has one parent who is, or if deceased was, a citizen of the nation the team represents, as evidenced by a passport or other documentation satisfactory to World Baseball Classic Inc. and the IBAF; or
The player has one parent who was born in the nation or territory the team represents, as evidenced by a birth certificate or its equivalent
I would guess one of Piazza's parents was born in Italy.