Well that's what I think but I try to understand OO perspective on this. I'm not exactly sure whether their ecclesiology is the same as ours. Many seem to be more open-minded than EOs.
I don't think there is such a thing as an OO ecclesiology, or an EO ecclesiology. I think there is only Orthodox ecclesiology. Unfortunately people, in both Communions, disagree about what that is.
There seems to be a mindset that either the EO are the Church, or the OO are the Church, and the Church can't be wrong, so it has to be one or the other, and anyone who says maybe it's both is labeled an Anglican (Branch Theory). But this seems to me to be borrowed RC ecclesiology making a straw man of Orthodox ecclesiology to call it Anglican and wrong.
I believe that the Greek Orthodox Church and the Coptic Orthodox Church are not Churches. A Church, an ecclesia, is a gathering of Christians, a community, a household, not a bureaucratic administrative institution.
A Church is a diocese, centered around a bishop. "Where the bishop is, there the Church is". Patriarchates are just synods of bishops, with a metropolitan or archbishop or patriarch as president. But that president is the president of a synod of Churches, not of a superchurch. Neither he nor the synod have authority to interfere in the local affairs of a Church, i.e. a diocese. They only decide together in love common issues.
The Churches that meet in a local synod are in Communion with on another automatically, since they all commemorate the same Patriarch, i.e. they are all in Communion with that Patriarch.
But what makes the Coptic Patriarchate in Communion with the Indians or any others? Historically, different patriarchates would exchange letters of Communion, agreeing to provide sacramental hospitality to each other's flocks, this is how they were in Communion.
But if two local Churches broke Communion with each other, this has never meant that one or the other is THE Church, and the other is not. In fact, both Churches might be in Communion with the larger Community, just not with each other. There are human misunderstandings that cause divisions that need healing--divisions within the Church. Even if there is a clean break of Communion, it does not mean that one or the other is or is not the Church. They can reconcile, as has happened in history, and one does not rebaptise and reordain the other, they just carry on, one Church restoring communion with the other.
How were they not two branches? Because the Church is not divided into bishoprics, or patriarchates. The Church is simply not divided. A local Church is not a part of the Church, it is the Church. The Church is the Body of Christ that spans all time and space, encompasses all Christians in all times and all places, all cultures, languages and classes. This is the meaning of Catholic, not world-wide. When two or three are gathered in His Name, around the Eucharistic table, the Church breaks into time and space, and that local community is present at the one Liturgy, united with all Christians in all Churches who are participating in the same Liturgy in all times and places. So even if they are separated from Communion from one another through ignorance, then they are not branches or parts, they are local communities that still participate in the unity of the Church, though through our sin that unity is not manifested to the world.
Now, if a group goes into heresy, then they are cut off from the Communion of the Church, anathematized. This does not mean that we know that when they pray the Liturgy they are not united in the same heavenly Liturgy, in the Body of Christ. It means that we find them defective, and so we cannot say they are a sure manifestation of the Church, or are surely a manifestation of the Church. So we cut them off, cast them out so that they may repent and others may not be scandalized. But this doesn't mean we say we are the Church, the Body of Christ, and they are not. The Church is not an institution, it is a mystery, it is the Body of Christ, and we know that we in the Orthodox Church surely participate in her in the Liturgy, but we cannot say about others.
So, when the Eastern Orthodox met the Anglicans, who presented themselves as Orthodox, as an Apostolic Church that broke from Rome and maintained Apostolic Christianity, it was perfectly normal that the reaction was not "we're the Church, so they can't be, let's convert them", but "we've found lost brothers we didn't know about". So it was perfectly natural that the Greek Patriarch sent a letter to the Anglican Archbishop thanking him for granting Sacramental hospitality to his people in North America where there were no Churches. It was perfectly natural that they should talk, and work towards reunion, not conversion. But when in those talks it became clear that the Anglican position was not as they had made out, that they were not Apostolic as claimed, that they were not a sure manifestation of the Body of Christ, of the Church, then it was perfectly natural to remain separate from them.
This is what has happened between the EO and the OO. We were separated for politics, and any differences in Christology we had have been worked out. It doesn't matter if one was wrong or not then, if they made an error and repented, we should heal the schism and be reunited. We should let the world know we are His by our love for one another. There is no excuse to remain separate now, out of fear of saying we were wrong about each other, out of fear of falling into branch theology, of saying that the there were two Churches... the EO and the OO are not Churches, they are groups of local Churches that participate in the One Church.
So if there are Catholic diocese in parts of the world that are free from the errors that came to Rome through ambition, it does not seem so outrageous to me if Orthodox local Churches and local Catholic Churches there recognize in each other the truth, and Commune. But if it is just a false unity with different beliefs, and only a common belief that belief doesn't matter, that Orthodoxy doesn't matter, then it is clearly wrong. I don't know the situation enough to know.
There is no Church of the 3 councils, or the 7 councils, or the Pope. There are only local Churches that either maintain the Apostolic faith and practise, and are in Communion with some other local Churches and not others, and there are local Churches that do not maintain the Apostolic faith, but follow traditions of men. Some like the Protestants reject even the priesthood and the Liturgy, so they are very clearly not local Churches, they are just gatherings of believers, but they can never be Churches without a bishop and the Eucharist. The RC have clearly deviated from the Orthodox faith, so we must remain separate. But the OO and the EO, if we hold the same faith, and participate in the same heavenly Liturgy, should not fear Communing together and having unity because of a wrong idea about what the Church is that makes us fear that saying so would mean the Church was wrong or there are two Churches, that simply isn't Orthodox ecclesiology.
I believe that what I believe is the Orthodox ecclesiology. But then, everyone with a different opinion also believes they are correct. This is a topic that needs to be explored much more. So many of the things we do wrong stem from bad ecclesiology.