We focus on explainability as a desideratum for automated decision-making systems, rather than only models. Although the explainable artificial intelligence (XAI) paradigm offers an impressive variety of solutions to increase the transparency of automated decisions, XAI contributions rarely account for the complete systems—social and institutional environments—where models operate. Our work focuses on one such system in the domain of social welfare, which increasingly turns to automated decision-making to carry out targeted digital surveillance. Specifically, we present a case study of a black-box machine learning model previously used in a major Dutch city to support its officials in the task of detecting fraud. Employing analyses established in the field of system safety, we identify five types of hazards that could have occurred after the introduction of the model. For each of them, we reason about the potential value of XAI interventions as hazard mitigation strategies. The case study illustrates how the deployment of models may impact processes that exist far upstream and downstream from their decision logic, making explainability and/or interpretability insufficient to guarantee the systems’ safe operation. In many cases, XAI techniques may only be able to reasonably address a small fraction of hazards related to the use of algorithms; several major hazards that we identify would have still posed risks if the system had relied on an interpretable model. Thus, we empirically demonstrate that the values, which lie at the heart of XAI research, such as responsibility, safety, or transparency, ultimately necessitate a broader outlook on automated decision-making systems.