Do shia believe in present Quran

There are many sects within Shi'ism itself, but the mainstream Shii belief is they use the same Quran as Sunnis, though they interpret many verses differently (political differences on the most part).

[For the sake of citing a reference: http://en.wikipedia.org/wiki/Shiism]

It is true that there were some variations in the Qurans present at the time of Uthman, but no sources mention anything about Shii ideas being burnt. Shiism didn't even exist back then. Am I right?

Beliefs of Shia about the present Qur'an

1 Mi ibne lbrahim~-Qiimmi relates from Ab a Zar'e Ghaffari that the Holy Prophet, in conunenting on the verse "Yauma Tabyazzat wojoohohum", said: On the Resurrection Day my people will come to me under five different standards and I will ask the group under each standard about what they have done with the Two Precious Legacies which I left among you, ie. The Thaqalain? The people under the first standard will reply, "Of the two precious things which you left behind, the greater one we have distorted and thrown behind our backs and ignored, and the lesser one we opposed or hated" The group under the second standard will reply, "Of the Two Pre~ious Ones, the greater (the Qur'an) we distorted and tore to pieces and went against it, and the lesser one we opposed and waged war against it"
2 Thne Taoos and Seyyed Nairnatullali Jazairi, the two prominent Shia traditionalists relate a lengthy tradition that the Holy Prophet declared to Hozaifatibnul Yamaani that the person who profanes the sanctuary of Islam would make people deviate from the path of God, would distort His Book and would alter the Sunnat (traditions) of the Holy Prophet

3 Sa'd ibne Abdullah-e-Qummi quotes the Fifth Holy Imam of the Ahiul-Bait, Muhammad ibne Ali Al-Baqir, that the Holy Prophet called th~ people of Mina and said: Oh people! I am leaving among you Two precious things and if ye adhere to these ye will never go astray: namely the Book of God and my AhIul- Bait. And, beside these Two, here is the Ka'ba, the Sanctuary (the Holy House) Then the Holy Imam said' "The Book they have distorted, the Jtrat (the AhIul-Bait) they have killed and the Ka'ba they have destroyed, and all the things of God that were with them they threw away and detached themselves from them."

4 Shaikh-e-Sadooq asserts in his Khisaal, through Jabir ibne Abdullab-e-Ansari, that the Holy Prophet said that on the Resurrection Day three entities would complain, the Quran, the Mosque and the Itrat The Quran would say, "Oh my Lord! They distorted me and tore me to pieces." The Mosque would say, "Oh my Lord! They kept me and spoiled me." The Itrat would say, "Oh my Lord! They killed us, drove us out of our homes and made us wander hither and thither."

5 The tradition told by Kaafi and Sadooq from Mi ibne Sowaid says that he wrote to the Seventh Holy 'main, Musa ibne Jafar al-Kazim, while he was in prison and received the following reply: "They were ent"usted with the Book of God and they distorted and altered it."
6 Thne Shhhr Aashoob tells that the Third Holy 'main, Husain ibue Mi, while addressing the enemy army on the day of Aashoora, said:
Ye are of the same rebellious party and the remnant of the infidel allies (against the Holy Prophet), and the remnant of those who threw out the Book (the Holy Qur'an) and were inspired by Satan and the gang of criminals and of those who distorted the Book
7 In the book, Kacirnilur Ziyarah it is said that the Sixth Holy 'main, Jafar ibne Muhammad As-Sadiq, prescribed the following prayer for the pilgrims who entered the shrine of the Holy Irnam~ Hnaain: "Oh God! Curse those who deny Thy Prophets, destroyed Thy House (the Ka'ba) and distorted Thy Book."
8 It is said that the Sixth Holy 'main~ Jafar ibne Muhammad As-Sadiq, said, "The masters of the Arabic language distorted the Word of God from its proper place."