Automatic SOAP note generation can ease the documentation burden on physicians, but existing reasoning methods often omit clinically important information and generate unsupported content. Progress in Thai is further hindered by the lack of publicly available datasets. We propose ASCRIBE, a physician-inspired reasoning framework that ascribes a clinical-significance level to each extracted atomic fact in the conversation before summarization, making a general-purpose LLM a more reliable scribe. We also release ThaiClinicBench, the first de-identified Thai clinical summarization benchmark of real encounters, together with a synthetic training corpus derived from real clinical notes. As a prompt, ASCRIBE outperforms chain-of-thought prompting on GPT-5.4 and Gemini 3.1 Pro across the physician-aligned LLM-judge metrics and improves on standard prompting by up to 10.3 points on the completeness LLM-judge metric. As a GRPO reward, it enables a Gemma-4-E4B model trained solely on synthetic data to match Gemini 3.1 Pro in factual precision and surpass it in completeness. Code and data can be found at https://github.com/loolootech/ascribe.