In contrast to the Nes-Nisayon Theory (NNT), stands the Myth-Moshol Theory (MMT). Whereas NNT assumes that all Torah must be read as literal truth, MMT posits that often the Torah contains allegorical passages. The supporters of NNT tend to believe that the Torah must not be allegorized, whereas the supporters of MMT tend to believe in the scientific evidence, and are uncomfortable with the ideas of nes and the fake 'old' earth that NNT requires. MMT is widely held in more broad minded orthodox institutions, but quite likely would be regarded as heresy in more fundamentalist environs. Orthodox Jews of limited exposure tend to be quite ignorant of MMT, and its widespread acceptance in the more broad minded areas of Orthodoxy.
For example, MMT would say that the stories in the beginning of Breishis are clearly mythological, desgined to counteract the prevailing Babylonian / Summerian mythologies of their day. The theory is explained by Nahum Sarna in his book 'Understanding Genesis', and Umberto Cassutto in his books 'From Adam to Noah' and 'From Noah to Abraham'. Cassutto brings a particularly detailed explanation, showing pasuk by pasuk how prevailing Summerian notions were dismised by the Torah, and replaced with monotheistic ones. It is probable that Sarna got this theory from Cassutto, though its also clearly written in the popular Soncino Hertz Chumash, in the notes section at the end of the book of Genesis, which dates back to the 1930's. (Its likely that Rabbi Hertz got this from elsewhere too, maybe Christian bible scholars. More research is required here).
There is also a parallel to this in the Rambam, with the Rambams well known views on the Korbanos. The Rambam holds that the korbanos were only created to wean away the Israelites from their own idolatrous practices, and was but a temporary phenomenon. Similarly, the stories in Breishis could have the same purpose.
Although both Sarna and Cassutto seem to imply human authorship of the Torah, from a religious perspective, their theories need not be dismissed out of hand. It is possible to say that ancient Israelite scrolls were passed down to Sinai, at which point, with a few edits and changes, they were incorporated into the Torah under G-ds direct command. A more liberal reading of the Rambam ikkarim would still fit. There is even some midrashic support for this latter view, see this article by Rabbi Gil Student. However, in order to reconcile Science completely, it clearly would not be feasible to say that Noah or Adam actually wrote these scrolls, since according to NNT it is highly unlikely that these characters actually existed (at least in the form that we imagine). More likely they written by others, perhaps with some level of divine inspiration.
A more orthodox twist to this theory is one that I call 'moshology' as opposed to 'mythology'. According to this version, the stories in Breishis were not designed just to give the Israelites their own monotheistic mythology in contrast to the polytheistic mythologies of the day, but in fact (or also) contained deep eternal truths about G-d and the universe, and G-ds relation to man. In this view, these stories were absolutely 'written' directly by G-d, but still need not be literally true. This would be similar to the Zohar's view, which says that the Torah is just a shell, and only fools do not delve behind the external form. Its probable though that the Zohar did not mean to imply that the basic simple peshat of the pasuk was wrong, just that there were additional deeper peshatim. However according to MMT, the simple peshat would be quite wrong. Either way, it seems that many of these deep secrets have been lost, or at least are not accessible to the average man.
There are plenty of sources in the Rishonim for taking Breishis allegorically, not least of which is the Rambam in Moreh Nevuchim in his famous passage on the creation story. The Rambam says that he would have explained Breishis as not meaning that the creation was at a point in time, but only refrained from doing so because he did not believe the eternal universe theory (prevalent in his time) was accurate. Fundamentalists would however reject this approach, and consider this line of reasoning to be foreign to our (current) mesorah.