Shortages of critical medical supplies during the COVID-19 pandemic have turned global value chains (GVCs) in personal protective equipment (PPE) into a political lightning rod. Some blame excessive outsourcing and foreign dependency for causing shortages, thus urging greater state intervention; others applaud GVCs for their flexibility and scaling up of production, while blaming states for undermining GVC operations. Using policy process-tracing and monthly trade data of seven PPE products across the US, Europe, China and Malaysia, this paper goes beyond the binary debate of either the 'failure' or 'success' of GVCs to show when and under what conditions states interacted with GVCs to produce mixed outcomes in provisioning countries with PPEs. We identify interactions between the type of state intervention and two key structural features of GVCs - geographic distribution of production and technological attributes of the product. Conceptually, the paper demonstrates the mutual constraints of states and GVCs, and highlights structural factors involved in the relationship. Looking to the future of GVCs, we caution against wholesale declarations that GVCs should be abandoned or maintained, instead concluding that paying attention to GVC structure, states and their interactions are crucial.