Personalized interpretation of medical reports has emerged as an increasingly important need among patients. Addressing this need requires both evidence-grounded medical factuality and context-dependent patient communication, yet existing medical vision-language tasks do not adequately capture these dual requirements. To bridge this gap, we introduce Patient-oriented Medical Report Interpretation (PMRI), a novel open-ended multimodal generation task that requires models to explain medical reports in accurate and accessible language based on a user's query and dialogue history. These two objectives differ fundamentally in their verifiability, yet remain tightly coupled, making them difficult to optimize jointly under conventional supervised fine-tuning and holistic reinforcement learning paradigms. To address this challenge, we propose G-CARL, a grounded, checklist-aligned reinforcement learning framework that combines multi-source retrieval for atomic claim verification with context-aware, instance-specific weighted checklists for response coverage, providing structured supervision for factuality, user-demand satisfaction, and expression quality without constraining response diversity. We further construct MMedReport, a real-world PMRI benchmark, along with a clinician-designed three-dimensional evaluation protocol. Extensive experiments demonstrate that G-CARL consistently outperforms existing post-training baselines in overall quality, claim-level precision, and checklist recall. Pairwise preference evaluation by clinicians further confirms that G-CARL produces interpretations that are more accurate and better aligned with patient needs.
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