The Controversy Over the Third Secret: Objections and Responses | Fr. Andrew Apostoli, C.F.R. | Appendix D from Fatima For Today: The Urgent Marian Message of Hope
The Third Secret has been dealt with in two chapters in this book. Chapter 8 presented the content of the Third Secret as Lucia, Francisco and Jacinta saw it revealed to them. Chapter 16 presented how Sister Lucia wrote the Third Secret on a separate manuscript and then placed it in a sealed envelope. The chapter also traces what popes John XXIII, Paul VI and John Paul II did after reading it.
The Third Secret was first made public at the Beatification Mass of Francisco and Jacinta Marto on May 13, 2000, in the Cova da Iria where the secret was originally revealed to the three children on July 13, 1917. Unfortunately, controversy created by certain objections surrounded the Third Secret almost from the moment it became public. We will look at each main objection separately, and offer a response to each.
Objection: The original Third Secret was written on one sheet of paper.
Many clerics who were familiar with the original text, including bishops who worked with popes John XXIII and Paul VI, said that the Third Secret was written on a single sheet of paper (e.g., Cardinal Alfredo Ottaviani, who read the Third Secret with Pope John XXIII). 
The controversy came about when on June 26, 2000, the Vatican released a copy of Sister Lucia's handwritten text in a four-page format.  Though there are several possible ways a single sheet of paper can be turned into more than one page (written on both sides, folded and written on multiple sides, etc.) or copied onto more than one page, some critics said that the Vatican copy could not have been made from the authentic text and that some other document exists that contains the real Third Secret.
The Vatican copy of Sister Lucia's handwritten manuscript appears in the document The Message of Fatima prepared by the Congregation for the Doctrine of the Faith. In the introduction, the secretary of the Congregation at the time, Archbishop Bertone, stated: "There is only one manuscript, which is here reproduced photostatically." Sister Lucia herself confirmed the validity of the Vatican text. Archbishop Bertone and Bishop Seraphim de Sousa of Leiria met with Sister Lucia at her Carmelite convent in Coimbra, Portugal, on April 27, 2000. The Archbishop presented two envelopes to Sister Lucia. The first or outer envelope contained the second envelope, which held the Third Secret. Touching it with her fingers, Sister Lucia said, "This is my letter." Then, while reading it, she said, "This is my writing."  When asked if this document was the one and only Third Secret, Sister Lucia answered, "Yes, this is the Third Secret, and I never wrote any other." 
We have additional proof from Sister Lucia that the photocopy of the Third Secret was authentic. She met again with Archbishop Bertone on November 17, 2001. A communique about that meeting carried this most important point:
With reference to the third part of the secret of Fatima, [Sister Lucia] affirmed that she had attentively read and meditated upon the booklet published by the Congregation for the Doctrine of the Faith [The Message of Fatima] and confirmed everything that was written there. To whoever imagines that some part of the secret has been hidden, she replied: "everything has been published; no secret remains." To those who speak and write of new revelations, she said: "There is no truth in this. If I had received new revelations, I would have told no one, but I would have communicated them directly to the Holy Father." Objection: The text of the Third Secret released by the Vatican contains no words attributed to the Blessed Virgin Mary.
The message of the Third Secret was not conveyed in words by our Lady, but in the various visions the children saw. Our Lady spoke simply by her actions, as when she prevented the fire from the flaming sword of the angel from touching the earth and consuming it. Archbishop Bertone explained:
The part of the text where the Virgin speaks in the first person wasn't censored, for the simple reason that it never existed. The text these people talk about just doesn't exist. I am not toeing some party line here. I'm basing my statement on Sister Lucia's own direct confirmation that the Third Secret is none other than the text that was published in the year 2000. Objection: The Vatican's copy of the Third Secret contains no information about a nuclear holocaust, a great apostasy, or the satanic infiltration of the Catholic Church.