What you need to keep in mind when looking at any biblical references are these things:
Firstly, the Bible is the witness of the Church. It is impossible for the Church to misinterpret anything in it.
Secondly, there are primary interpretations for the various passages and there are secondary interpretations. The primary interpretation is the one the author intended to convey to us. And what did Matthew intend to tell us? That Jesus was giving the keys of the kingdom to Peter and that he would build his Church upon him.
And thirdly, secondary valid interpretations do not trump the primary ones. So it can be said that Jesus was building his Church on Peter’s faith, but also on Peter himself, which is the primary interpretation. It’s both and, not either or.