Large vision-language models (VLMs) often benefit from chain-of-thought (CoT) prompting in general domains, yet its efficacy in medical vision-language tasks remains underexplored. We report a counter-intuitive trend: on medical visual question answering, CoT frequently underperforms direct answering (DirA) across general-purpose and medical-specific models. We attribute this to a \emph{medical perception bottleneck}: subtle, domain-specific cues can weaken visual grounding, and CoT may compound early perceptual uncertainty rather than correct it. To probe this hypothesis, we introduce two training-free, inference-time grounding interventions: (i) \emph{perception anchoring} via region-of-interest cues and (ii) \emph{description grounding} via high-quality textual guidance. Across multiple benchmarks and model families, these interventions improve accuracy, mitigate CoT degradation, and in several settings reverse the CoT--DirA inversion. Our findings suggest that reliable clinical VLMs require robust visual grounding and cross-modal alignment, beyond extending text-driven reasoning chains. Code is available \href{https://github.com/TianYin123/Better_Eyes_Better_Thoughts}{here}.