Medical vision-language models (VLMs) show strong performance on radiology tasks but often produce fluent yet weakly grounded conclusions due to over-reliance on a dominant modality. We introduce a context-aligned reasoning framework that enforces agreement across heterogeneous clinical evidence before generating diagnostic conclusions. The proposed approach augments a frozen VLM with structured contextual signals derived from radiomic statistics, explainability activations, and vocabulary-grounded semantic cues. Instead of producing free-form responses, the model generates structured outputs containing supporting evidence, uncertainty estimates, limitations, and safety notes. We observe that auxiliary signals alone provide limited benefit; performance gains emerge only when these signals are integrated through contextual verification. Experiments on chest X-ray datasets demonstrate that context alignment improves discriminative performance (AUC 0.918 to 0.925) while maintaining calibrated uncertainty. The framework also substantially reduces hallucinated keywords (1.14 to 0.25) and produces more concise reasoning explanations (19.4 to 15.3 words) without increasing model confidence (0.70 to 0.68). Cross-dataset evaluation on CheXpert further reveals that modality informativeness significantly influences reasoning behavior. These results suggest that enforcing multi-evidence agreement improves both reliability and trustworthiness in medical multimodal reasoning, while preserving the underlying model architecture.