Properly managing healthcare data is a complex endeavor that must balance the requirements and interests of many stakeholders. In this paper, we present the findings from a panel discussion with healthcare professionals and academics, who elaborate on the current situation in healthcare data management as well as the future role that blockchain could play in this sector. Based on the findings of this panel, we structure the research field of healthcare data management and provide numerous avenues for future research. The outcome is a framework that highlights the important role of healthcare data and puts them into context. From a patient's perspective, we specifically elaborate on trust and privacy as well as the expected benefits. Additionally, four important data aspects are identified: integrity, security, interoperability, and, finally, sharing and transfer. We also outline the importance of current problems and derive several relevant and timely research questions that build the foundation of a research agenda for blockchain-driven innovation in healthcare data management. In summary, the framework will inform practitioners of blockchain's potential in healthcare and structure the area for researchers, who are called upon to investigate the respective topics in greater detail.