"He had built His Church on the foundation that was this man [St. Peter]."
Looks like the foundation was the promise to Israel ingrafted by faith, not any man except Christ Jesus.
Rom. 11:24, "For if thou wert cut out of the olive tree which is wild by nature, and wert graffed contrary to nature into a good olive tree: how much more shall these, which be the natural branches, be graffed into their own olive tree?"
So many metaphors, so many theories.
I do think that the Book of Acts spells out Jesus' words that He would use Peter to get the Church started. The Acts can be divided into 2 sections: (1) Peter, (2) Paul.
After Paul's death history tells us that Peter again became more active.
However, just because Peter was the point man in getting the church started it does not follow that he started the Roman Catholic Church. That's an unsupportable leap of logic.
To be sure "upon you I will build my Chruch" is a metaphor. He is a man, not a truck of ready mix. I do not see a foundation metaphor though in the "olive tree" passage.