According to him most of his people considered the Unction service on Holy Wednesday as a cleansing & healing service and this took the place of a private Confession for them! I know other Greeks that have implied the same thing.
I know of at least one Greek Catholic priest who teaches such a thing, as well (although in the same breath also exhorts in the strongest terms the need for regular private confession). He was even called into the papal nuncio's office once about it and told to knock it off.
The Mysterion of Holy Unction in fact does include the forgiveness of sins. The Apostles themselves taught this:
"Is any sick among you? let him call for the elders of the church; and let them pray over him, anointing him with oil in the name of the Lord, and the prayer of faith shall save the sick, and the Lord shall raise him up; and if he have committed sins, they shall be forgiven him." (James 5:14-15)
Isn't this an Apostolic Teaching?
I don't think I have the full service of Unction in front of me, but I do have a Priest's Prayer Book (the one I referenced earlier), and it has an Unction Service "for the home" (i.e. abbreviated). In it, at the prayer of the sanctification of the oil, it asks (pp. 172-173):
"... send down your Holy Spirit and sanctify this oil; and may it convey upon your servant(s) (N), who is (are) anointed with it, complete deliverance from his (her) (their) sins, and the inheritance of the Kingdom of heaven."
Then, in the Prayer of Anointing the Sick person (pp. 174-177) it says:
"Holy Father... heal your servant(s) (N) from his (her) (their) bodily and spiritual sickness, and restore him (her) (them) by the grace of your Christ; through the intercessions..."
Finally, he includes a Prayer of Forgiveness, similar to that found in the sacrament of Holy Confession (similar in substance, with a statement about holding the open Gospel Book over their head instead of laying on hands).
On the GOARCH website they have the prayer of Blessing the Oil from the sacrament of Holy Unction,:http://lent.goarch.org/holy_wednesday/learn/
"Prayer of the Oil
O Lord who, in thy mercies and bounties, healest the disorders of our souls and bodies, do Thou, the same Master, sanctify this Oil, that it may be effectual for those who shall be anointed therewith, unto healing, and unto relief from every passion, every malady of the flesh and of the spirit, and every ill; and that therein may be glorified Thy most Holy Name, of the Father, and of the Son, and of the Holy Spirit, now and ever, and to the ages of ages. Amen."
(In the Greek text, for "malady" they use the word molismou, a derivative of which is used in modern Greek for Pollution....)