No, Jesus spoke the truth.
It’s our interpretation of what He said that is faulty.
If we take Him at His word, then the Roman Catholic Church has it wrong.
If we take Him at His Word:
“And I tell you, you are Peter, and on this rock I will build my church, and the gates of hell shall not prevail against it. I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven.”
The Church has it right. Even though you disagree. Perhaps you are illustrating your fallibility here?
:)