To interpret The Tale of Genji as an individual artifact about specific people would largely miss the point of such an epic work. Much like the epic poems of Western history, Genji is more of a story about Japan itself, the rejected son of a royal king who begins a new dominion in the mountains. It's the epic story of feudal japan, the vices and virtues of passionate, larger-than-life characters, so essentially, it's an epic myth of sorts.
In Japan, the idea of family honor is much more serious than the words sound to an American, for instance. Their idea is much more spiritual, as if ancestors are alive in heaven, watching the earth to see how their legacy is honored by their sons and daughters. You can see this basic idea expressing itself in the plot of the story, because the back half of the novel is something of that effect: Genji as an overlord and guide for his wandering descendants in their pursuit of greatness. Therefore, a story about grandfathers and great-grandfathers is much like a Western myth about the gods.
This is also evident in the archetypal quality of many of the characters. For instance, the king with a concubine motif is consistent with Jesus Christ's ancestor David, who gave birth to the royal bloodline with Bathsheba. The idea of a rejected person having to wander around is found in the Odyssey, in the Old Testament account of the fall of man and man's return to paradise. The idea of an ancestor watching the lives of his children from above is also very common in world mythology. The story is highly, highly archetypal, so interpret its meaning would be like interpreting life itself.
That sounds like big language, but it's basically just academic language for the idea that because the story covers so much terrain, and because it's so human and tangible as a story, that it reminds the reader of many stories they've already read before.
