If This total narrative about the Prophet he just randomly narrated some verses, i think there comes a lot of questions,
like how this book come into place, why some verses refer itself?? as a book?? even when its not released completely? so was this planned well before to be as a book?, or the author knows well, it will be released as a book and should have asked someone to write it down or even wrote it himself?
To my understanding the quranic verses that says it as the book, the 'kitab' actually means the law giving examples/stories of the past, to be used as guidance. So i dont think the total compilation is the kitab, instead the stories and examples in it.
Telling is actually reciting, telling the truth, is what true recital is all about. The verses are the different teachings/rules(aayats) taken from the story/message.
Corruption of the kitab, is actually can be seen as corruption of the story/message.
People of the Kitab, could be those who base their religion based on the collection of stories of the past.The Christians.
So Quran has its own stories as revealed by the prophet in his own understanding and that i think that is the main part of the Quranic kitab and the message it gives.