In this paper we reflect on the ethical challenges that arise as a result of efforts to improve healthcare through analyses of large-scale datasets. We focus in particular on the importance of ensuring that the systems that manage sensitive data are both trustworthy and trusted, and whether/how this might reasonably (and ethically) be achieved. We consider the fragility of the concept of data ownership in the absence of trust—indeed, in the absence of trustworthiness—and the impact that this has on people’s perceptions of digital society. We reflect on case examples from our research; and the case of care.data and the public backlash that led to its closure in 2014. These cases highlight the fear and uncertainty that surround data sharing practices in general, and how this has caused challenges in the process of designing digital health systems.