I feel this tendency to come up with an evolutionary explanation for basically everything under the sun is not needed.
The ultimatum game is the ultimate test of fairness, and chimpanzees passed the test by going for the fair options.
Frans de Waal is a Dutch/American biologist and primatologist. He teaches at Emory University and directs the Living Links Center for the Study of Ape and Human Evolution, in Atlanta, Georgia. He is known for his popular books, such as Chimpanzee Politics (1982), Bonobo: The Forgotten Ape (1997) and The Age of Empathy (2009). He has been elected to the National Academy of Sciences and the Royal Dutch Academy of Sciences.