Machine learning technologies are increasingly developed for use in healthcare. While research communities have focused on creating state-of-the-art models, there has been less focus on real world implementation and the associated challenges to accuracy, fairness, accountability, and transparency that come from actual, situated use. Serious questions remain under examined regarding how to ethically build models, interpret and explain model output, recognize and account for biases, and minimize disruptions to professional expertise and work cultures. We address this gap in the literature and provide a detailed case study covering the development, implementation, and evaluation of Sepsis Watch, a machine learning-driven tool that assists hospital clinicians in the early diagnosis and treatment of sepsis. We, the team that developed and evaluated the tool, discuss our conceptualization of the tool not as a model deployed in the world but instead as a socio-technical system requiring integration into existing social and professional contexts. Rather than focusing on model interpretability to ensure a fair and accountable machine learning, we point toward four key values and practices that should be considered when developing machine learning to support clinical decision-making: rigorously define the problem in context, build relationships with stakeholders, respect professional discretion, and create ongoing feedback loops with stakeholders. Our work has significant implications for future research regarding mechanisms of institutional accountability and considerations for designing machine learning systems. Our work underscores the limits of model interpretability as a solution to ensure transparency, accuracy, and accountability in practice. Instead, our work demonstrates other means and goals to achieve FATML values in design and in practice.