Most accounts of global justice, whether they be nationalist, cosmopolitan or Rawlsian approaches, tend to focus on the obligations of developed/rich countries toward poor/developing countries or well-ordered societies toward burdened societies. But the question to identify what developing/poor countries themselves owe to their own citizens in this respect or how unfavorable conditions into which burdened societies are trapped impact the assessment of their obligations toward their own people have received little attention. Theorists of global justice tend to assume that poor countries need help and implicitly presume that their obligations toward their own citizens, if any, are weaker than developed countries’ and may be limited to accepting help or assistance from developed countries and managing it efficiently and fairly. Relying on the African context and using the case of the human right to health (care), this paper presents a theoretical agenda that will challenge that implicit presumption. The focus here is on the big picture on how we must think about the obligations that African societies themselves have regarding the right to health of their own people. This paper assumes that there is a (human) right to health (care) and defends four claims. First, we cannot achieve global justice, especially in the domain of health (care), unless African societies stop dumping their primary responsibility to protect the fundamental rights of their own people on rich countries. The global justice debate will benefit from more emphasis on the fact that the responsibility to provide for the most important needs of African citizens primarily rests on African societies themselves (the ‘Duty-Dumping’ Counter-Argument). Second, the obligations of African societies should also be assessed and grounded on their potential abilities and not exclusively on their actual ability (the ‘Potential Ability’ Argument). Third, what African governments owe to their own people in the domain of health (care) is to build efficient economies within fair political institutions since only this economic-political combination can help support all pressing health (care) and other needs and meet the necessary trade-offs that come along (the ‘Economic-Political’ Argument). Fourth, any international assistance in the domain of health care should be less a transfer of any kind of wealth (paternalism) than the restriction by rich countries from designing an international economic and political order which undermines the capacity of African societies to meet their health (care) obligation toward their own citizens (the ‘International Unfairness’ Argument).