I've been challenged with that same statement by someone I came to love and respect. "The Bible is not the Word of God, Jesus is". It was someone who knew the Scriptures well, though, and quoted them often.
I think the statement is really a reaction to the way the Scriptures have been used (misused) to promote various propositions, divisions, and power structures over the person of Christ himself.
Personally, I don't like the way we talk about the Bible as a single book - all nice and neat in one cover. I think cannonization was one of many historical rabbit trails that did far more damage than good. Before that, believers just had to dialog together about their various writings to test them and think them through. Most believers have no idea how or why the books of the Bible were selected, or how messy and controversial that process really was. The result is that people forget how to listen to the Spirit of Christ in patient fellowship with one another as they test all things together.
Jesse, I understand your point about people reacting to the misuse of scripture. I however think the best reaction is the correct use of scripture. I also agree with the importance of understanding the process of canonization. Sadly, not many people want to invest the time.