Bp. Williamson's major premise here is quite correct, actually. These Eucharistic and other miracles not only have ever been held by the Church to be incontrovertible proofs that Her doctrine on the Real Presence is correct against the contentions of the Protestant heretics, but even to prove the veracity of the Christian Faith itself. Miracles, in general, are "a manifest sign of the divine origin of the Christian religion" (Oath against Modernism) and to be accounted among "the most certain signs of revelation", for "demonstrating as they do the Omnipotence and infinite knowledge of God, they are well suited to the understanding of all". (First Vatican Council, on Faith and Reason). Therefore, continues the same dogmatic decree, "Moses and the Prophets, but especially Christ Our Lord Himself worked several absolutely clear miracles".
Transubstantiation is a particularly stupendous example of the miraculous. Christ the Lord visibly and perceptibly transformed water into wine at the Wedding of Cana to prefigure in a supremely fitting way the transubstantiation of bread and wine into His body and blood; there the miracle was performed to kindle faith. (St. John the Apostle writes that this was the first miracle Jesus worked and His Apostles began to believe in Him.) The miracle of grace that happens every hour of every day on Christian Altars presupposes it; and rewards true Faith in that mystery sufficiently proven to those strong in their Faith by the Word of Truth, (The Angelic Doctor beautifully writes what is usually summarized in English as "I believe every Word the Son of God has spoken, than Truth's own Word there is no truer token). In transubstantiation, the first substance ceases entirely to exist; in itself an act of the divine Omnipotence. For this reason, it is commonly taught that the natural power of all men and Angels together, nay even of the Blessed Virgin Herself, is entirely insufficient to effect transubstantiation. The Saints and Doctors in their lofty writings are lost in contemplation of this incredibly dignity Christ our Lord has placed in His priests. How immeasurably happy and eternally grateful for this infinite gift should be the man called to serve God in the traditional Catholic priesthood, as well as all who by faith know and adore Him in the Eucharist and receive Him in Holy Communion through their ministration. Anyway, in transubstantiation, the second substance - in the case of the Eucharist, Our Lord's own Most Holy Flesh and Heart's Blood - begins to inhere in the accidents of the first. Neither of these could conceivably be effected by any mere creature, God alone, and specifically His Omnipotence, must be the efficient cause of each and every act of transubstantiation.
Modern controversies which I don't want to enter into at the moment aside, here's a traditional 8th century miracle for us all to rejoice in.
"In 1970-'71 and taken up again partly in 1981 there took place a scientific investigation by the most illustrious scientist Prof. Odoardo Linoli, eminent Professor in Anatomy and Pathological Histology and in Chemistry and Clinical Microscopy. He was assisted by Prof. Ruggero Bertelli of the University of Siena.
The analyses were conducted with absolute and unquestionable scientific precision and they were docuмented with a series of microscopic photographs.
These analyses sustained the following conclusions:
The Flesh is real Flesh. The Blood is real Blood.
The Flesh and the Blood belong to the human species.
The Flesh consists of the muscular tissue of the heart.
The Flesh is a "HEART" complete in its essential structure.
...
The Flesh and the Blood have the same blood-type: AB (Blood-type identical to that which Prof. Baima Bollone uncovered in the Holy Shroud of Turin)."
http://www.therealpresence.org/eucharst/mir/lanciano.html
It was also worked by Christ the Lord, as the link explains, in response to a "doubting Thomas" in the 8th century A.D. In His gracious goodness, the Almighty sees fit sometimes to encourage weak faith by such miracles. Perhaps many millions of Catholics today, weak in their faith, informed of such miracles, would believe in the Real Presence while they otherwise would not, perhaps to eternal loss - and so, even in this crisis in His Church, the loving and adorable Heart of Our Savior in Infinite Mercy did not deem fit to leave these millions without a miraculous proof of His Real Presence in the Eucharist.