When you say,"twisting" do you mean like the way you have to do when you try to tie Peter to the Catholic Church by bridging a 300 year span of time?
In differentiation, there are two separate words being used in the verse to punctuate what Jesus is saying. If he had chosen The self same two words and not made a differentiation, you *might* have something. That is the uphill battle you must fight against the scripture, not against other factions, sects or denominations (depending on your choice of words); but against scripture. That the words do not mean the same thing is illustrated in their definitions. Their definitions are different - substantially.
Further, the entire subject being discussed is the importance of Jesus and of the proclamation of faith in him.. not Peter. The congregation was not built on Peter, it was built upon a Confession of faith in Jesus being the son of God. That is the church. Peter was one among many charged with the responsibility of laying that foundation. After that, God built upon it and the congregation grew from house to house, city to city, province, country to the world. Peter is not the foundation of any church - nor was he meant to be.
And it cannot be said that Peter alone was handed the 'keys to the kingdom'. That is your reading of it. Go back and read the whole chapter. Taking a single sentence from George Bush speaking to the nation not too long ago doesn't paint the entire intent and meaning in the speach. One cannot yank a single verse out of the Bible and read it in such a fashion either - though many wish to do so regularly. I think you'll find that the RCC teaches the self same thing. We just don't find it practicing such things when it presents a problem to foundational belief - that all goes straight out the window in favor of philosophical tenets.
When you start changing the focus of individual pieces of scripture, it changes the meaning of everything around it as well - robbing the meaning and diminishing the rest of the work. It reduces knowledge to knowledge of philosophy and ignorance of the word of God. Lack of knowledge of God's word causes people to perish. Thus the ultimate result of playing word games with scripture is condemning people to hell because ultimately they are destroyed for lack of knowledge of God's word. And that is precisely why twisting scripture for personal agendas is so sickening and outlawed expressly in the texts of the Bible. It is why so many warnings are given against false doctrine that even at the time of Peter, Paul and John as creeping - even flooding in. And much of what is described in II Peter about false doctrine sounds an awful lot like what we can still see even today - and not just in the RCC.
Since there is room for misinterpretation in this particular passage iIt is important to seek "two or three witnesses". Here is what the bible says about the term "rock" since we can agree that Peter nor another interpretation is in fact a rock, then the term is used figuratively.
Deuteronomy 32
3 Because I will publish the name of the LORD: ascribe ye greatness unto our God.
4 He is the Rock, his work is perfect: for all his ways are judgment: a God of truth and without iniquity, just and right is he.
15 But Jeshurun waxed fat, and kicked: thou art waxen fat, thou art grown thick, thou art covered with fatness; then he forsook God which made him, and lightly esteemed the Rock of his salvation.
18 Of the Rock that begat thee thou art unmindful, and hast forgotten God that formed thee.
1 Samuel
2 There is none holy as the LORD: for there is none beside thee: neither is there any rock like our God.
2 Samuel 22
2 And he said, The LORD is my rock, and my fortress, and my deliverer;
3 The God of my rock; in him will I trust: he is my shield, and the horn of my salvation, my high tower, and my refuge, my saviour; thou savest me from violence.
Romans 9
32 Wherefore? Because they sought it not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone;
33 As it is written, Behold, I lay in Sion a stumblingstone and rock of offence: and whosoever believeth on him shall not be ashamed.
1 Corinthians 10
4 And did all drink the same spiritual drink: for they drank of that spiritual Rock that followed them: and that Rock was Christ.