The Church of God General Conference affirms a non-papal interpretation of Matthew 16:18. The COGC understands the 'rock' to be either Peter's faith/confession or Christ himself, not Peter's office or person as a hierarchical authority. This reading rejects Roman Catholic papal theology and apostolic succession.

The COGC's emphasis on Scripture as the ultimate authority and its polity as congregational with some higher oversight means that no individual human is understood as having supreme ecclesiastical authority. The Church is built upon the revelation of Christ (as confessed by Peter's faith) and is guided by Scripture and the Holy Spirit, not by a papal office.