Peter had answered the question by Jesus that was, who do you say I am. Peter replied that Jesus was the Son of the living God. I think that fact of who Jesus was, that was to be the rock the Church was to be built on.
You may be correct but my suspicion is that this interpretation really became popular post-Reformation and is the way so many folks (no attack intended towards you my friend) try to get out of problem texts when it comes to religion/Christianity. I personally have no problem with the notion being that Peter is the rock. I think non-Catholics are wrong in looking for some ways to get around Catholicism's teaching of the pope, and I also think Catholicism distorts the meaning as well. Keep in mind that in those systems you have two different means of authority - one deriving from individual interpretation of the Bible and the other arising from the assumption that God left us an infallible interpreter of the Bible.
No person reading without presuppositions or trying to get out of it would read this as Catholics and as many Protestants do. Even the Catholic has to run his theology through the filter of assuming the Magisterium is infallible (we'll set aside the obvious problem that even if we assume that, the claim has little merit since many religious bodies claim infallibility and.....more importantly.......even having an infallible interpreter(s) doesn't change the fact the choice of whom to believe is still a fallible choice).
I'm not saying anybody is wrong here, I'm just saying I think there's too much baggage here that folks are trying to disarm their opponents with that it makes the Scripture a tool for argument and not a guide for life.