It's a false premise - the "Rich American" has a duty to help those who are less fortunate (poor Africans), and that duty extends further than just quid pro quo transactions.
We don't know that. In any case, the example is too simplistic anytime there is a lucrative market in organs, there will be middlemen who coerce victims into donating. That will / does kill people, no doubt.
Whenever you're thinking about human systems, you need to think about how humans will game the system. Essentially, you're not facing a static adversary, but an adaptive, motivated one.