Evidence-based medicine promises to improve the quality of healthcare by empowering medical decisions and practices with the best available evidence. The rapid growth of medical evidence, which can be obtained from various sources, poses a challenge in collecting, appraising, and synthesizing the evidential information. Recent advancements in generative AI, exemplified by large language models, hold promise in facilitating the arduous task. However, developing accountable, fair, and inclusive models remains a complicated undertaking. In this perspective, we discuss the trustworthiness of generative AI in the context of automated summarization of medical evidence.