In every document the oecumenists put out that deals directly with the issue, 'branch theory' is rejected, the myth that they accept it is propagated by people with a clear agenda against the oecumenical movement. In the aritcle on oecumenical guidelines I posted Fr. Stephanopoulos said, 'The Church is one and remains one and visible in the historic Orthodox communion. However, it is painfully obvious that there is a difference between the faith-affirmation of the unity of the Church and the empirical fractured appearance of Christendom.' The Eastern Rite Papal Churches are called 'Sister Churches' not because we believe them to be part of the One, Holy, Catholic, and Apostolic Church, but rather because we acknowledge that the faith they profess, or at least the vast majority of it, is consonant with Orthodox Christian Dogma: the Statement is Brotherly and Emperical in nature, not Dogmatic or Ecclesiological. Concerning the recognition of Baptisms, Canon VII of the Second Oecumenical Synod accepts Arian Baptisms as Valid; are we to conclude with this that the 150 Most God-Beloved Fathers who Assembled in Constantinople in A.D. 381 regarded the Arians as part of the One, Holy, Catholic, and Apostolic Church? Just as the use of the term 'Sister Churches' does not compromise our Ecclesiology, neither does the acceptance of the baptism of certain Heretical (or Schismatic) sects; of course, if we were to strictly follow the Council of Carthage under Cyprian, we in the GOA would also be required to reject the baptisms preformed by ROCOR and even the OCA, rebaptizing those who wished to come to the GOA from either church, as neither is technically in communion with the Oecumenical Throne.
I'm aware that there are anti-oecumenical spokesmen in Canonical Churches, as well as amongst the old-calendarists (their posistion is actually a bit more reasonable than the old-calendarists, for if we were to give into the old-calendarist demands, we would be required to, as mentioned above, reject their Baptisms as invalid, as we already generally reject their priesthood). Concerning these people, they are free to hold this opinion, so long as it does not conflict with the official posistion of their Synod, to whose aruthority the entire local Church, including Bishops, must submit. Concerning Mt. Athos, the Patriarchate grants them a disproportionate level of indulgance because they are a Self-Governed Monastic and Theocratic State, though it should always be remembered by those on Mt. Athos and those around the world, that the Patriarchal Synod, not the Monks of Mt. Athos, have the authority to make decisions in regard to relations with other churches (be they Non-Chalcedonian, Old-Calendarist, Latin, Protestant, et cetera), and the rest of the Church is expected to accept and uphold these decisions.
Concerning 'oecumenical' vs. 'ecumenical' it's not so much of a differentiation between Greek and English as between the Greek '+++Ãƒâ€šÃ‚Â¦+Ãƒâ€šÃ‚Â¦++-ÃƒÆ’ +++Ãƒâ€šÃ‚Â¦+++Ãƒâ€šÃ‚Â¦+Ãƒâ€šÃ‚Â¦-ÃƒÆ’Ã‚Â®-ÃƒÆ’Ã‚Â©' and the french 'ecumenic' with the adjectival suffix '-al' added to the end of both. I actually love the English language, and am convinced that it is one of the wonderfully capable language and one of the most Linguistically Inetersting languages ever, with such diverse etymologies and the rapid and profound evolutions of grammar over the last thousand years: I have nothing against English, so long as it is not used in our Divine Services.