Digital Twins, due to their ability to simulate and predict complex systems, are set to transform healthcare by improving personalised medicine, potentially tailoring diagnostics and reducing treatment costs. However, as their effectiveness depends on the availability of large, high-quality and inclusive datasets, current challenges pertain to fragmented health records, underrepresentation of minority groups, and the risk of algorithmic bias resulting from flawed information. To address these issues, the concept of data altruism, as set out in the EU Data Governance Act, has emerged as a promising strategy to diversify and improve the data pools needed to train DTs. Nevertheless, these practices carry significant ethical implications and normative challenges. This article explores the potential of the adoption of data donation mechanisms to better medical DTs within the European context, taking the first steps in analysing related ethical challenges while highlighting the importance of data quality and equity.