I would say that that assertion is completely false.
When we think of literature, we often fail to realize that our understanding of it is rooted in Western ideas of learning and storytelling—that is, stories and verse written and transmitted to the masses through print. Though it is true that certain Asian cultures also had writing—paper was, in fact, invented in China around 100 BC—the act of telling stories and recording them for posterity is deemed a Western tradition.
Epic narratives, fables, and other tales did exist among other peoples on other continents, however, including Africa. Let's consider how this tradition existed in West Africa, for example.
Sunjata, a tale told among the Mandingo people (from what is now Mali), is one of the best-known African epics. The story was passed down by generations of griots since the thirteenth century. A 'griot' is similar to the troubadour of medieval Europe in that he was skilled in oral performance, reciting histories as epic poems or narratives. The griot differed from the troubadour in the sense that he remained rooted to his tribe and community, while the troubadour traveled from place to place transmitting poems and tales. Also, the troubadour's main function was to entertain. Storytelling was often accompanied with music. On the other hand, the griot's main function is "to preserve, record, and transmit the history of their people" (Hill 35). Finally, griots still exist in some West African communities, whereas troubadours ceased to exist after the invention of the printing press around 1440.
Sunjata is similar to the French and English courtly romances told during the same period. Sunjata was a real person. He was a Mandingo warrior-king who led a revolt against Ghana, a declining empire, in 1200 CE. Ultimately, he united Mali's twelve kingdoms, creating one of the most powerful empires the continent has ever known.
Though this tale is rooted in history, it is regarded as literature because every griot who has told the tale through the ages has improvised its details. There are, in fact, four published versions of the epic and all of them are different. Moreover, as with all epic tales, there are mythical elements to Sunjata. For example, our hero is born crippled and, from birth, is threatened by mortal enemies. The antagonist in the epic is an evil sorcerer king named Sumanguru, or "Soumaoro Kante" in other accounts. Ultimately, Sunjata defeats Sumanguru by attacking his protective life force, a crowing white cock, with a magical counterforce, "a cockspur in a poisoned weapon (arrow or gun)" (Hill 36).
This narrative deals with some of literature's ageless themes: good vs. evil, heroism, justice vs. injustice, and overcoming adversity. In terms of form, it follows the patterns we see in other literary traditions. There are characters, including a protagonist (main character) and an antagonist (an enemy, or someone who works against the protagonist). There is also a fixed setting and a plot which introduces a situation, brings that situation to a climax, and then provides a clear conclusion/resolution.
Thus, Sunjata, like Western narratives, is a work of literature. The only difference is that griots did not write it down until very recently.
Source: Hill, Patricia Liggins. Call and Response: The Riverside Anthology of the African American Literary Tradition. Boston and New York: Houghton Mifflin Company. 1998. Print.