Talmudic and Islamic scholars cross-fertilized in legal matters because they lived in the same mercantile society. But the two traditions didn’t just overlap when it came to the law. Story telling was an art in the folklore-rich Arabian world.Sounds interesting, although if early Islamic lore incorporates demonstrable material from Dead Sea Scrolls traditions, I have not heard of it.
Amongst the few things that the patchwork of Jewish sects in the Arabia Peninsula had in common was a repository of folklore. The Talmud had drawn on some of it, but there was much more which it did not absorb, including literature linked to the secessionist priestly sect at Qumran, who are best known as the authors of the Dead Sea Scrolls. Early Islam had drawn in Jewish converts who recounted these Dead Sea tales along with everyone else, based on their memories of legends they had heard as Jews.
UPDATE: A reviewlet of Freedman's book by Rabbi Harvey Belovski has also been posted at the Jewish Chronicle: The book they couldn't suppress. The story of the classic text that shaped Judaism - the Talmud.