True, and it is He, Himself, who is the Rock on which His church is built, not Peter.
Jesus IS God, God with us. The faith profession is the foundation stone connecting us to The Rock of Heaven, Jesus . When Jesus spoke to Peter Jesus was standing there before Peter. We know Jesus was not calling Peter the rock because He knew Peter would not only open his mouth in a few seconds and utter a satanically inspire rebuke to Jesus but also deny Jesus three times before morning arrived on Friday! So Jesus had to be referring to the profession Peter made which connects Peter to THE Rock. Paul also confirms this profession as the faith connector to THE ROCK in Heaven when Paul writes of the stone the builders rejected. The stone is faith, the very thing that had departed from Israel and made it possible for them to not even see God with them. Faith in The Christ is the rock to which Jesus referred because that rock is laid upon a foundation which yields Gold, silver, and precious stones to be revealed at the mikvah cleansing/Bema Seat in Heaven. That rock allows God to be with us, indwelling, even unto the end of the Age.