From Fr. W. Joseph Boyd. Don't let the title fool you. An interesting take on why the Branch Theory Fact is true, regardless of what the Orthodox and Roman Catholics say. From the article:
As an Anglican, I can sincerely state my admiration for Eastern Orthodoxy and my confidence in the apostolic, catholic and truly doctrinally orthodox nature of its positions and its effective and valid sacraments. It was mainly through the Orthodox witness that the Anglicans rediscovered the ancient fathers and re-appropriated an apostolic independence from the Pope as a prerogative of the local catholic church. In this way we are indebted to Orthodoxy. The only thing we deny to the Orthodox, as the Orthodox would deny to the Pope, is control over God's grace by later political or canonical mechanisms. Apostolicity and ordination confer the Grace upon which councils are based, not the councils providing Grace upon which bishops are made. The Seven Ecumenical Councils state the mind of the Church in the conditions and contexts of the day and must be interpreted within them. They are extremely valuable as standards of Church life and administration, but are not "infallible" without this contextualization or equal in importance to Scripture, which reveals the source of all church authority. Therefore, we must contend that there is Apostolic Grace, true episcopacy and effective sacraments that are not defined by the Byzantine Communion. While the Orthodox hold "fullness of Grace", they do not limit grace or define its borders. We believe that we, too, are a local expression of the One, Holy, Catholic and Apostolic Church. This is what Anglicans believe and see as biblical and self-evident, but what Orthodox fundamentalists can never accept, because they apply St. Cyprian's maxim "there is no salvation outside of the Church" not to the local catholic, apostolic, sacramental Church, but to the Orthodox Communion as an institution. We would argue that in St. Cyprian's time, such an institution did not exist and what he meant was the Apostolic Succession of the local catholic church and faithfulness to the Nicene Faith. Thus, our interpretive grid would be different, and our conclusions opposed, which is truly unfortunate, since we share the same faith in Christ as our Lord and Savior.