Discharge summaries, particularly the Brief Hospital Course (BHC) section, are critical for continuity of care but remain time-consuming for clinicians to compose. We introduce GraphFact-Summ, a graph-augmented summarization model that integrates unstructured clinical notes with structured data (e.g., labs, medications) to generate accurate and concise BHC summaries. Our model encodes sentencelevel and event-level information using a heterogeneous graph transformer, and applies a factual-gated decoder trained with reinforcement learning to minimize hallucinations. Evaluated on over 330,000 admissions from MIMIC-IV, GraphFact-Summ achieved a ROUGE-L of 0.430 and factuality of 91% based on alignment between generated summaries and structured clinical events, outperforming BART and Clinical-BART while maintaining a lower hallucination rate (11.0%) and shorter length ratio (0.96). Temporally held-out records (2020-2022), it sustain strong performance, with a ROUGE-L of 0.425 and a factuality score of 90%. Human evaluation by clinicians further confirms that the summaries are concise, accurate, and clinically useful. These results highlight the potential of GraphFact-Summ to support real-time summarization in electronic health record systems while reducing documentation burden.