It remains unclear whether agentic augmentation (iterative tool use, code execution, or retrieved memory) improves over single-pass VLM inference for medical image interpretation. We present a systematic quantitative evaluation of the Recursive Language Model (RLM) framework on a multimodal medical task, comparing three pipeline architectures (P1 direct vision, P2 iterative RLM tool use, P3 model-written code agent) across four retrieval-augmented memory conditions on 100 CheXpert Plus chest X-rays, scoring with CheXbert (14-label classification) and GREEN (radiology-specific LLM judge). Three findings emerge: (1) direct vision outperforms both agentic variants; the RLM loop consumes 7-9× more tokens without adding task-relevant information when its only tool calls the same VLM; (2) retrieval consistently helps, but the optimal pool size depends on metric and pipeline: top-5 is the sweet spot for direct-vision report quality (GREEN +37%), while 24 retrieved cases further benefit pathology classification (CheXbert +50%) and can improve GREEN for agentic pipelines; and (3) qualitative analysis shows code agents with a pretrained classifier succeed when it returns confident pathology scores but fail on normal cases where it returns noise-floor outputs, illustrating that tool quality, not framework complexity, determines outcome.