Why do some Christians take 2 Timothy 3:16 to mean the entire Bible is "God breathed"?

2 Timothy 3:16 says, "All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness." Most Christians I have known believe this means the entire Bible is inspired directly from the spirit of God. But, when Paul is said to have written this, there was no "Bible;" the only "Scripture" that existed was what Christians today view as the Old Testament. The Gospels had not been compiled yet, and Paul's writings were only letters. Most Christians with whom I have raised this issue believe that God inspired Paul to write this statement so that, even though the Bible did not exist yet, Christians in the future could take faith that the entire Bible is authentic. However, there is no evidence whatsoever to support this claim, and it seems as though it is just a poorly-thought out attempt to explain an inconsistency with traditional Church doctrine. Any thoughts?