One of the most prevalent rationales for public healthcare policies is a human right to healthcare. Governments are the typical duty-bearers, but they differ vastly in their capacity to help those vulnerable to serious health problems and those with severe disabilities. A right to healthcare is out of the reach of many developing economies that struggle to provide the most basic services to their citizens. If human rights to provision of such goods exist, then governments would be violating rights without doing anything wrong. I argue that such variable ability to provide healthcare depends not only on financial resources, but on institutional capacity, and that the latter represents a more fundamental challenge to the existence of a human right to healthcare than previously recognized. This challenge does not imply that government has no obligations to protect and improve the health of their citizens, but that it is best to think of such obligations as generated by conventional rights, namely rights arising from local legal and social conventions, which require governments to pursue health-related moral goals such as reducing suffering, closing opportunity gaps for the disadvantaged, and preventing the spread of contagious diseases. We need not think of such moral goals in terms of human rights.