Facts and errors about the Pieces
Without strong evidence I would take what happens on screen as canon, but if we cannot do that we should come up with a simple, consistent theory of what mistakes were made and then either describe the history as happening the right way or delete the history altogether.
Part 1 of the theory: from Pawn of Shadows to the end of All Fear the Freak the animators mistakenly showed the piece Velma held (which should have been #2, from the Darrow house) as piece #1, from Mayor Jones. The word "Fuego" was actually on the Darrow piece.
Part 2 of the theory: the flashback of Friar Serra at the end of Theater of Doom was incorrect. It should have showed pieces #4 (found in the cheese) and #6 (found underwater), not #4 and #5.