The Waldensian tradition rejects the Catholic interpretation of Matthew 16:18 as establishing papal supremacy or a succession of papal authority through Peter. The Waldensians, emerging from medieval dissent and aligning with Reformed Protestantism, understand the 'rock' to refer either to Christ Himself or to the faith-confession that Peter articulates.

The Waldensians emphasize that Jesus is the only head of the Church; no earthly authority (pope, cardinal, or bishop) can claim supremacy over the Church or infallibility in doctrine. The 'keys of the kingdom' granted to Peter are understood as spiritual authority given to all believers and apostles to proclaim forgiveness of sins through Christ and to teach the Gospel — not as institutional authority concentrated in a papal office.

Historically, the Waldensian rejection of papal authority was a central point of their medieval witness and their persecution. In affirming the Scripture principle (sola scriptura) and the sufficiency of Christ as the Church's head, the Waldensians deny that Matthew 16:18 establishes any hierarchy that would place Peter or his successors above the apostolic college or the broader Church.