Majority-vote LLM ensembles improve accuracy monotonically with ensemble size when agents are homogeneous samples of the same prompt (Li et al., 2024). We test whether this holds for four heterogeneous clinical-role prompts on one frozen MedGemma backbone, across binary tumor detection, tumor subtyping, MS, and stroke triage. Our comparison is against single-agent triage: we ask whether role-diverse voting clears that bar, not whether it matches sampling diversity, since we do not run a paired homogeneous-sampling forest. On a paired 500-image evaluation per task, a four-agent forest does not reliably beat single-agent triage: significantly worse on binary tumor (both stages) and MS end-to-end, indistinguishable on tumor subtyping and stroke. Pairwise error correlation between roles is far from independent on every task (φ = 0.43–0.75 vs. φ = 0 under independence), explaining why voting fails to average errors out. Roles diverge behaviorally on the easiest task but collapse onto a shared “normal” bias on the two hardest, so voting cannot recover sensitivity no member has. Dissent rate, a candidate escalation signal, is valid on two tasks, uninformative on MS, and inverted on stroke, where agreement is less reliable than disagreement. These results argue against assuming role diversity on a shared backbone helps by default, and for task-conditional validation before deployment.