How can a book I don't really know be my authority?

I've watched a lot of discussion online recently about biblical inerrancy and the authority of Scripture. An article by Australian theologian Michael Bird caused no small amount of discussion when shared on a Facebook group for discussion among scholars in my national church fellowship.

A couple of days later, I read the following statement in an article about biblical authority and divisions in American Christianity:

Perhaps in certain parts of academia – and in ministerial training in some denominations – historical criticism caused some to question the authority of the Bible, but for more than a century after the Civil War, the reading preferences and church affiliation choices of millions of American Protestants suggested that respect for the Bible’s authority continued undiminished, even if biblical literacy was not quite what it had once been. 

Note that last phrase: even if biblical literacy was not quite what it had once been.