Few recent developments have captured the human imagination as much as those within the field of artificial intelligence (AI). The increasing pervasiveness and ubiquity of AI affect both individual lives and society at large. Yet the human rights concerns raised in connection to AI have primarily concentrated around infringements of enumerated discrete rights, such as to privacy, non-discrimination, and freedom of expression and information. While it is important to examine the discrete rights under threat, a fundamental disconnect is present at the foundational level between human rights and AI, because AI systems increasingly challenge the notions of how, by whom, and what human rights violations are being committed. This paper takes a problem-finding perspective and argues that the conceptual foundations of the human rights protection framework are facing a serious challenge. The legal-positivist framing of the discrete rights themselves is examined through an analysis of the misaligned harm typology between the objects of human rights protection and the threats posed by AI systems. The paper highlights three main misalignments, from the perspective of saliency, temporality, and causality of harms, and argues that these misalignments challenge the structural enabling conditions for the exercise and meaningful protection of human rights.