High-precision document parsing in domain-specific scenarios, such as medical documents, remains challenging due to complex layouts, specialized terminology, and strict field-level exact-match requirements under noisy supervision. As a result, existing OCR pipelines and general-purpose vision–language models (VLMs) often fail to deliver reliable key–value extraction in practice. We propose a noise-aware post-training framework that adapts general-purpose VLMs for high-precision document parsing without assuming clean annotations. The framework learns robust extraction behavior from noisy supervision through training-driven label refinement and a staged RL-to-SFT post-training strategy that balances robustness and precision. Experiments demonstrate that VLMs adapted with the proposed framework consistently outperform strong baselines under noisy supervision.