I have noticed an attitude of suspicion also. Here is something interesting from the fourth edition of the Enchiridion Indulgentarium (Manual of Indulgences USCCB 2005). Latin Catholics encouraged to do eastern prayers and all Catholics granted indulgences for these.
See 23 Preces Orientalium Ecclesiarum, if you can read Latin, or see my rough translation below.
http://www.vatican.va/roman_curia/t...c_20020826_enchiridion-indulgentiarum_lt.html
23
Prayers of the churches of the East
Catholicity of the church by nature ensures that, “each individual part or the Church contributes through its special gifts to the good of the whold Church, so that the whole and each part increase” (Lumen Gentium No. 13) in regard to all the spiritual gifts of Divine generosity: from thence the prayers from the various traditions of the East have spread, even among the faithful of the Latin rite, especially in recent years, and with considerable advantage to religious piety, whether public or private use.
§ 1 A Plenary Indulgence is granted to the Christian faithful who sing (devoutly recite) the Akathistos hymn or the Office of the Paraclesis in the church or the oratory, and / or in the family, in religious communities and in the associations of the faithful and in general, when several of the faithful are gather to some honorable purpose. In other cases, the indulgence will be partial.
But in regard to Akathistos, when we sing the hymn for a plenary indulgence to be acquired, it is not required that the recitation be entire, but it is sufficient that continuous recitation is done of an appropriate part according to lawful decrees of custom.
Among the Christian faithful of the East, where the practice of these devotions does not exist, other similar exercises in honor of the Blessed Virgin Mary, according to the statutes established by the patriarchs, enjoy the same indulgences.
§ 2. The Partial Indulgence is granted to the faithful who, for the time and occasion of some prayer recite devoutly one from the following: A Prayer for the giving of thanks (from a tradition of the Armenians); an evening in Prayer, Prayer for the dead (from the Byzantine Tradition); Prayer of the sanctuary, Prayer «Lakhu Mara," or the «To thee, O Lord" (from a tradition of the Chaldeans); Prayer to the incense, glorified at Prayer to the Mother of God Mary (from the Coptic Tradition); A Prayer for the remission of sins, A Prayer for the acquiring the following of Christ (from a tradition of Amharic); A Prayer for the Church, he has completed the Prayer Liturgy of the (from the Maronite Tradition); Intercessions for the dead from the Liturgy of the S. James, (from a tradition of the Syrian-Antioch).