Yes, Sacred Tradition is that which has its origin from Christ and/or His Apostles.
The issue becomes more than each community, who received “a Scripture” directly from an Apostolic source. Each community must accept the other Scriptures that were delivered to **other ** local communities.
I would point to St. Irenaeus as an important Apostolic source for defending the true Scriptures. He defended the “fourfold” Gospels, when many Christian communities held one over the other. Maybe because they were more confident, as you allude, that their origin was directly from an Apostle. But this did not ensure the other Scriptures. For this, they needed to trust Tradition. But not just any Tradition. A Sacred Tradition, which St Irenaeus upholds is affirmed in the See of Rome.
You see, I am talking about accepting an entire Canon. In order to do so, one must rely on a church making a decision, based on tradition and it’s own authority to make that decision. In Catholic language, it is called Sacred Tradition and Magisterium. So our rule of faith is dependent on Sacred Scripture, Sacred Tradition, and Magisterium.
