Uninspired Canonical Books?

Source: Sid Z. Leiman, The Canonization of Hebrew Scripture: The Talmudic and Midrashic Evidence (Hamden: Archon, 1976).

The rabbis distinguished between books of the Bible that defile the hands and those that do not. Many argue that they were disputing which books were canonical--the canonical books defile the hands, whereas the non-canonical ones don't. The problem with this view is that a rabbi who denies that (say) Ecclesiastes defiles the hands may elsewhere quote Ecclesiastes as authoritative. We see this sort of phenomenon in rabbinic literature. Ergo, Leiman contends that the issue is not canonicity, but inspiration. The inspired books defile the hands, whereas the uninspired books do not.

I wonder how "uninspired" books made it into the canon. Was it because the rabbis (or the Jewish community) believed they had something to teach us, even if they're not the direct word of God? Ecclesiastes, for example, is a profound look at how a rich man coped with his own mortality. His skepticism about an afterlife doesn't have to be authoritative for us doctrinally, however, since Ecclesiastes is not the word of God (in Leiman's interpretation of one rabbinic perspective).

This is one rabbinic view, but I'm not sure if it's the Christian one. II Timothy 3:16 says, "All scripture is inspired by God and is useful for teaching, for reproof, for correction, and for training in righteousness" (NRSV). Paul (or, for liberal scholars, "Paul") apparently doesn't distinguish canonicity from inspiration, as if there are uninspired books in the biblical canon. As far as he's concerned, all the canonical books are inspired.