Actually, Kolo, thank you for stating this. It goes without saying. There are no Orthodox churches where I am, but I watch EWTN Mass at least several times a week. I attended the Mass for the late Pope JPII in a Catholic Church but did not participate in the communion, of course. If I were on a death bed, and no Orthodox priest were available, I would do the same thing as you said you would -- and for the same reasons: confession, sacraments, prayers. But anyone other than a Orthodox/Catholic priest, I would only ask for his/her prayers.
That's because the only authority any bishop/minister may have is through direct succession leading back to an Apostle of our Lord. The Lord gave the Church and the power to bind and loosen only to the Apostles. No Apostolic succession, no Church. Period. There is only One Church, and anything other than Orthodox or Catholic version of it is not a church as far as I am concerned.