Doesn't St. Basel the Great play a role in this too?
Indeed he does.
Here is a patristic viewpoint -from Saint Basil the Great.
Notice the typical balance of the Church Fathers - while the principle
of no Sacraments and no Apostolic Succession outside the Church is
clearly enunciated, Saint Basil also states very clearly that for the sake
of the good of the Church "economy" may be used if it is thought necessary
in the case of Baptism.
Epistle to Amphilochius (of which the "First Canon" of Saint Basil is a
shorter version)
---- "It seemed best to the ancients-I refer to Cyprian and our own
Firmilian-to subject all of these-Cathari, and Encratites, and
Hydroparastatae-to one vote of condemnation, because the beginning of this
separation arose through schism, and those who had broken away from the
Church no longer had in them the grace of the Holy Spirit, for the imparting
of it failed because of the severance of continuity.
"For those who separated first had ordination from the Fathers, and
through the imposition of their hands possessed the spiritual gift; but
those who had been cut off, becoming laymen, possessed the power neither of
baptizing nor of ordaining, being able no longer to impart to others the
grace of the Holy Spirit from which they themselves had fallen away.
Therefore they commanded those who had been baptized by them, as baptized by
laymen, to come to the Church and be purified by the true baptism of the
Church.
"But since on the whole it has seemed best to some of those in Asia that,
by economy for the sake of the many, their baptism be accepted, let it be
accepted."
-oOo-
Note the word "economy" used here by Saint Basil with reference to
situations when baptism is not insisted upon. Saint Athanasius also uses the
word economy with reference to the reception of ther heterodox. I wanted to
point this out since there are modern theologians who mistakenly say that
the concept of "economy" was something created by Saint Nicodemus of the
Holy Mountain in the 19th century. Not so!
Now I think that all the Orthodox are doing is preserving the principles
which were enunciated by the Church Fathers and which were operative in the
early Church, principles which have faded from the mind of most Western
Churches. However, the East has had no Reformation or Counter-Reformation.
It has not had any codification of canon law such as The Catholic Church
had after Trent; so all the Orthodox can turn to is the teaching and canons
of the first millennium to provide guidelines and insights with regard to
modern questions which crop up today, including the matter of Baptism
and other Sacraments outside the Church.
Fr Ambrose