Actually each of the Patriarchates were free to choose the books of the Bible as long as, when read in the proper way (i.e. based on the oral traditions behind the said book), they didn't conflict with the doctrines of the Church. For instance, in the early Constantinople patriarchate's liturgical canon, the deuterocanon was not included (hence St. Jerome's objection to them being added into the canon). However, they considered them to be just as inspired as the rest of scripture (also validated by St. Jerome). Just because something is not in the canon does not guarantee that it is not inspired. For example, in some of the Eastern Catholic and even some of the older Eastern Orthodox canons you will not find the book of Revelation. It's not because they didn't consider it inspired, but because they didn't consider it canonical, or necessary for liturgical purposes - which was, essentially, the purpose of the Bible. The Bible was not meant to be a stand-alone pillar, but a very important supplement to the liturgies of the real source of the faith - the Church, whose source is Christ.