Except in this case, the show is on the other foot. The absence is your provision of proof that there are so many forests of pieces of the true cross.
Deception can go both ways. Logically, that is also possibility. Therefore, there is no proof to the opposite as well.
I need to prove nothing to you. You haven”t proved anything to me by citing a 19th century hack and his crumb counting. No one will ever know what his biases were, what pieces he rejected or what his travel budget limited in the way of his search. Sorry but there are 8 or 9 skulls of John the Baptist out there as well as all kinds of bones, teeth, clothing etc purportedly belonging to saints. The business was huge.
Guess away and believe what you will. Clearly, the credibility of the human is undiminished since at least the middle ages.