Nice response. I also like the use of the phrase "approved by Christ." Indeed, you could use the analogy that the Catholic Church considers itself the "authorized" Church, while the Orthodox Churches are "unauthorized" Churches. After all, the only major remaining sticking point for us is an acknowledgement of the actual, not symbolic or honorific, primacy of Roman pontiff, which is what we consider a divinely instituted authority. Orthodoxy, not accepting this, is an "unauthorized" Church in that sense (along with the OO, Polish National Catholic Church, Assyrian Church, Armenian Apostolic Church, and---possibly---some traditional branches of Anglicans and Old Catholics).
[My opinion here:] The sacraments do not stop in such Churches, though they are likely not efficacious for the unrepentent people responsible for the original separation (as they would be for any unrepentant Catholic too). Most Orthodox and most Catholics were, of course, blameless in the division of centuries ago. While their Churches remain, they still receive grace through the sacraments via God's great love and mercy.