Communion is not simply a legal agreement, and it cannot be extended by wordplay but only through authentic unity of faith.
Sola Scriptura does not take from but reinforces the authority of the Catholic Church. The Holy Ghost works in His Church to bring us closer to the Scriptures.
As seen in the Church Fathers, even if St. Peter is the Rock of Matthew 16, the modern papal doctrines do not follow. Rather, a proper equality of bishops is taught by the Sacred Scriptures and the Church Fathers.