They were referring to the Eastern Orthodox in schism. Not to treat them as a monolithic group, since there are at least five distinctly different Churches represented by the term “Eastern Orthodox” but there are at least some of them who do not recognize the validity of Holy Orders or the Sacraments as practiced by the Catholic Church in union with Rome, in any of its Rites; they don’t only pick on the Latin Rite or the Western Church.
And the fact that they aren’t in full communion with the Pope.
And we don’t intercommune with them, either, ordinarily.
That is true in the sense that it is not a regular practice. However, if we do find ourselves in an area where a Latin Rite or some other Rite in communion with Rome is not available, then, under those circumstances can we receive Holy Communion from an Eastern Orthodox Church.
Now, when I lived in Austin, there was (and still is) a Greek Orthodox Church, St. Elias. Although I never set foot in it (I probably should have, at least just to see what it looked like), it would not have made any sense for me to receive Holy Communion from their Church since Austin has a plethora of Catholic Churches. But, if I were visiting Greece and was not in an area where there were any Latin Rite or Eastern Rite (communion with Rome) churches, then, I would have to go to a Greek Orthodox Church, out of pure necessity.
I can’t say the same for the Anglicans, though. I did manage to set foot inside St. David’s because Cardinal Cassidy (who was one of the point prelates on ecumenism) had been invited to speak at the Episcopal ecclesial community. However, it was just that, a speech. There was no real prayer service involved. However, to go to one of their services just to go and then receive their version of communion is something that the Church is against. In fact, doing so would have caused scandal, especially if those present knew that I was Catholic.
You are right in the first point you raised. The Russian Orthodox Church is highly suspect of us and has accused us of trying to invade their turf, so to speak.
I guess my bone of contention was that in the Anglican analogy, there needs to be a distinction regarding validity. We don’t recognize the validity of their ordinations. Hence, without a valid ordination (which lacks Apostolic Succession since it was broken), there can be no valid Eucharist.