Near Does Not Mean Easier to Reach: A Matched Diagnostic of Accessibility Ranking

Geometric proximity and network accessibility can recommend different navigation targets. We study this distinction through matched corridor graphs whose coordinates stay fixed while one passage closes. Each of 48 generated map triplets contains a baseline, a closure that reverses the optimal target, and a sham closure that preserves both target distances. All worlds remain connected. Exact graph inputs remove visual perception as an explanation for errors, and route certificates permit mechanical verification. In a locally run, four-bit Qwen3-4B evaluation, both baseline and rank-reversed choices are correct in 29.2% of triplets (95% interval: 18.2-43.2%) when coordinates are supplied. Both generated routes are optimal in only 14.6% of worlds. Adding coordinates has an inconclusive effect on paired accuracy, and rank-reversed worlds are more accurate than baseline worlds; the findings therefore do not support a simple proximity-bias account. Our contribution is a small, reproducible diagnostic combining correct change, correct invariance, and graph-verified routes, with preliminary evidence about compact language models rather than a claim about embodied agents generally.