Pervasive digitization and aggregation of personal health information (PHI), along with artificial intelligence (AI) and other advanced analytical techniques, hold promise of improved health and healthcare services. These advances also pose significant data governance challenges for ensuring value for individual, organizational, and societal stakeholders as well as individual privacy and autonomy. Through a case study of a controversial public-private partnership between Royal Free Trust, a National Health Service hospital system in the United Kingdom, and Alphabet's AI venture DeepMind Health, we investigate how forms of data governance were adapted, as PHI data flowed into new use contexts, to address concerns of contextual integrity, which is violated when personal information collected in one use context moves to another use context with different norms of appropriateness.