Dear Griego,
Yes, the theory that the Basilian Fathers took the Pochayiv Icon was once circulated, but has proven false. The original is still at the Pochayiv Monastery in Ukraine.
In fact, there is another miraculous Icon of Pochayiv there, an icon that depicts the Mother of God over the rock on which Her Footprint was imprinted.
This miraculous icon was sent to the Lavra from Kyiv in 1859 following an answer to the Kyivans' prayer to stop a cholera epidemic there.
One problem, as with other Shrines, is that Pochayiv is claimed by both Catholics and Orthodox, although it is certainly an Orthodox Shrine, and of this there can be no doubt.
But the official position of the Ukrainian Catholic Church today is to recognize it as an Orthodox Shrine and to say that Catholics share in the great veneration to it.
The three main Shrines of the Lavra are: The miraculous Icon, the Footprint of Our Lady from which holy Water flows and the relics of St Job of Pochayiv.
The Footprint is held in great devotion and the special Communion Loaves used there are stamped with the image of Our Lady's Footprint.
To venerate the Footprint, as is mentioned in the Way of the Pilgrim, is to ask Our Lady to guide our own footsteps in the path toward God.
As the OCA pages Orthoman has listed state, a monk and a shepherd by the name of Ivan Bossiy, saw the Mother of God in the midst of a flaming aureole on the mountain of Pochayiv, with a Crown and a sceptre.
She said nothing and after the apparition disappeared they found Her footprint imbedded in the rock over which She appeared and water flowed from it.
This is, in fact, the "Lourdes" of the East.
Anna Hoyska received the icon from a Greek Patriarch and donated it to the developing monastery where pilgrimages began in earnest immediately following.
The Church of the Holy Trinity is no longer there, but was built through the charity of the Domashevsky family. The only representation we have of it, in fact, is in the family portrait of the Domashevsky.
My ancestor, Auguste Yablonowsky, was also devoted to the Shrine and donated generously to the Lavra. My wife, Tanya, is a descendant of the Orthodox Metropolitan of Kyiv, Dionysius Balaban, who glorified St Job a saint in 1654.
On the back wall of the Cathedral there are represented 21 miracles of the Pochayiv Mother of God, one of which involved the curing of a blind Polish Catholic woman who later became Orthodox in thanksgiving.
There is also a beautiful Icon of the Choir of the Saints of Volyn: Sts. Stephen and Amphilochius of Vladimir in Volyn, St Theodore prince of Ostrih, St Juliana Olshanska, St Job of Pochayiv, St Macarius of Kaniv, St Yaropolk prince of Vladimir in Volyn.
(As a side-note to Paul - St Josaphat was also a saint from Volyn, but Catholic.)
There is a special Akathist to Our Lady of Pochayiv and to St Job of Pochayiv that St John of Kronstadt press has available.
The miracle of the repelling of the cannon-balls at Pochayiv through the Mother of God and St Job is celebrated with special popular songs.
The people came out and began singing the Akathist to the Mother of God (Annunciation) and having read the first Kondak, the miracle and apparition occurred. As a result, this Kondak is said as a separate prayer by Orthodox Christians to this day.
Also, it should be noted that a number of the Turks who witnessed this miracle became Orthodox Christians and Monks at the Pochayiv Lavra.
As a sidenote to our Pro-Catholic friend, Robert K.

- I'm not against the Basilians, Robert. I served in a Basilian Church for seven years as an altar boy.
The fact of their historic Latinization as a religious Order is simply that, something that applies to the Redemptorists and others. And I have Redemptorists in my family.
There are many among them who fight Latinization in their Order, such as Fr. Basil Zinko OSBM of Brazil who is very dedicated to the Byzantinization of the full Eastern Horologion, Fr.Julian Katriy, OSBM who has written so widely about the purity of Byzantine Church liturgical traditions and Fr. Meletius Soloviy, OSBM (+memory eternal!) who wrote so much about the same.
Metropolitan Ilarion Ohienko of the Ukrainian Orthodox Church attacked the historic latinizations of the Basilians at Pochayiv, their taking it over etc.
But he had nothing against the Basilians of this century insofar as their Ukrainian identity went, and indeed the Basilian Press at Zhovkva (where St Nicholas Zahorivsky, the Orthodox Hieroconfessor died) published a number of his literary works.
Again, I have never come across an Orthodox who was so defensive of the Ukrainian Catholic Church!
You are more papal than I, my friend. And I say that with the utmost of respect and fondness!
Alex