Here is a great way to look at it without causing too much conflict (I hope):
If your mother tells you something, you believe it. Your mother may not be inerrant but since when is being inerrant required to believe something? We listen to our relatives and friends who are not inerrant. The same was with the Apostles before the New Testament even existed.
This line of thinking where everything must be biblical is not very logical, think about it. If you were one of the people in Thessalonica when Paul came into town to preach and teach, you would be forced to reject him, because he is just a mere man speaking. This is how many Jews rejected the Gospel, they just did not believe because they had their Torah and rabbinic traditions and that was all there is to it.
Now before anyone is up in arms ready to torch me, I am saying that Paul and the other Apostles were inspired by the Holy Spirit yes certainly. However just because it is in the Bible, does not mean it is correct, there are instances where Job's friends were saying something, and where even the devil himself is recorded as saying something in the Bible. I doubt anyone quotes what the devil said as recorded in the Bible and says "Amen its true, it is in the Bible, God's word!". We know better than that.
The purpose of the Bible is not to be an idol or a god, but the purpose of the Bible is to LEAD US to Him who Himself is the resurrection and the life, and that would be Jesus Christ.
John 5:39 ""You search the Scriptures because you think that in them you have eternal life; it is these that testify about Me;"