Myth does not mean a false story in the sense that I think Andrew Sullivan used it. I think it is the same sense of the word that we find in the writings of C. S. Lewis. For example, Lewis wrote:
[T]he story of Christ is simply a true myth; a myth working on us in the same way as the others, but with this tremendous difference, that it really happened, and one must be content to accept it in the same way, remembering that it is God’s Myth where the others are men’s myths
Wikipedia, under Mythology offers this:
The main characters in myths are usually gods, supernatural heroes and humans. As sacred stories, myths are often endorsed by rulers and priests and closely linked to religion or spirituality. In the society in which it is told, a myth is usually regarded as a true account of the remote past. In fact, many societies have two categories of traditional narrative, "true stories" or myths, and "false stories" or fables. Myths generally take place in a primordial age, when the world had not yet achieved its current form, and explain how the world gained its current form and how customs, institutions and taboos were established.
The so-called truth of myth is not necessarily historical truth. In this sense the Tower of Babel is a myth. We cannot know if it was real, historically. There are some ancient ziggurat foundations, the Etemenanki ziggurat just south of modern Bagdad being one, that may be the foot of the biblical tower. Annie is right, Etemenanki is visible through the facilities of Google Earth.
It should be noted that the “Tower of Babel” is not mentioned in the Bible. It is the unnamed tower of the city of Babel or perhaps more correctly, Bāb-ilim, meaning gate of the gods, or maybe Balal, meaning confused or jumbled.
This discussion of myth makes me wonder if it would not be a good word to use for much of what we say about the shroud: the myth of flower images on the cloth; the myth of dematerialization; the myth that it is the real image of the real Jesus (or dare we say mythical Jesus).