An emerging issue in AI alignment is the use of artificial intelligence (AI) by public authorities, and specifically the integration of algorithmic decision-making (ADM) into core state functions. In this context, the alignment of AI with the values related to the notions of trust and trustworthiness constitutes a particularly sensitive problem from a theoretical, empirical, and normative perspective. In this paper, we offer an interdisciplinary overview of the scholarship on trust in sociology, political science, and computer science anchored in artificial intelligence. On this basis, we argue that only a coherent and comprehensive interdisciplinary approach making sense of the different properties attributed to trust and trustworthiness can convey a proper understanding of complex watchful trust dynamics in a socio-technical context. Ensuring the trustworthiness of AI-Governance ultimately requires an understanding of how to combine trust-related values while addressing machines, humans and institutions at the same time. We offer a road-map of the steps that could be taken to address the challenges identified.