Actually, since the past 30 or so years, the Roman Catholic Church will admit Eastern Orthodox Christians to their Sacrament of Holy Communion, if the bishop under whom is the individual approves such. The statement is written within the preface of the Missal.
No so for the Orthodox Church. The Eucharistic Service of the Orthodox Church, the Divine Liturgy, includes much focus on the unity of the faith and the manifestation of the Eucharistic community as the Body of Christ, surrounding Holy Communion.
From the Divine Liturgy:
"Entreating for the unity of the faith and the Communion of the Holy Spirit...";
"The Holy Things, are for the Holy" people of God;
"We have beheld the True Light, we have received the heavenly Spirit, we have found the true faith, worshiping the undivided Trinity..."
If you are not of the faith that is working synergistically to prepare and serve Holy Communion, which considers itself "the true faith," of which we pray for its "unity," i.e. unity of belief, you cannot intrude, and participate in it, as you do not share the belief of the faith, and are not part of the Eucharistic community, the manifestation of the Body of Christ.
One reason for the Orthodox practice of a priest or bishop being required to celebrate only one Liturgy per day, is so that "the Eucharistic community of believers," the "Body of Christ," worships together.
Fraternal, loving, brotherly relations are one thing; compromising "the faith," quite another.
So yes, if an Orthodox Church is not near an Orthodox Christian, peasant or not, quite unfortunately, he or she cannot receive Holy Communion. At least today, in addition to the maintenance of a prayer life, study of the scripture and other books of the church, anyone with internet access can at least view the Divine Liturgy to assist their spiritual well being, not to imply by any means that internet viewing of the Liturgy is in any way a substitute for participation in the Divine Liturgy and Holy Communion.