One point which may conflict with this idea is that bonobo brains are significantly smaller than chimpanzee brains - while in humans, culture seems to have made brains larger. Small brains are consistent with the bonobo domestication syndrome, though.
Key data which evaluating this hypothesis depends on involve comparisons of common chimpanzee vs bonobo cultural learning abilities.
There's some comparative data here. It says (on p.27) that bonobos use tools to acquire food much less than common chimpanzees do. Bonobos do have sophisticated social learning skills, though, as Kanzi demonstrates.
If bonobos are more like humans than chimps because they have more culture, then that would be a fantastic discovery from the perspective of students of cultural evolution. It would make bonobos a snapshot of the development of culture in progress - with common chimpanzees providing a baseline.