Those who think the Bible was written in the Persian period (and, of course, a couple of works actually purport to have been written then, but those are not the work that those making the claim are talking about) or later in the Hellenistic period have not spent much time looking at actual documents from that time purporting to be earlier histories. There is a wealth of difference between apocryphal accounts of Israelite history and biblical accounts.
Consider the apocryphal versions of Israelite history in Judith or 1 Esdras. Esdras actually garbles Persian history, putting the kings in the wrong order. Judith garbles the capital of Babylon. 1 Kings and 2 Kings, on the other hand, get their Near Eastern history correct. If these accounts were written when the apocryphal accounts were, how did they manage to get things right when the apocryphal accounts get so much wrong?