Clinical large language models are increasingly fielded as multi-agent teams, on the assumption that deliberation averages out individual error. It does not average out bias. Across a full factorial of five model families and four aggregation topologies on 120 real MIMIC-IV emergency cases under counterfactual demographic swaps, no configuration neutralizes the disparity: all 20 cells commit the direction of their agents' independent answers, giving Black patients more acute triage. Every model has a topology that amplifies its baseline gap, but which one varies by model, so no design is reliably safe or reliably amplifying: the disparity is relocated, never removed. Late-stage fixes fail: fairness instructions and demographic masking leave the gap untouched, and per-agent self-debiasing widens it, because the bias is already encoded in the agents' ordinary clinical numbers. We call this disparity laundering; the audits now applied to clinical AI, per model, per output, per version, can certify the parts but never the committed decision. Interventions close the gap exactly when they make counterfactual versions visible inside the system and pool them, through deliberation, into the committed decision. A diverse-perspective ensemble does both while keeping the team, with no retraining or architectural change: the disparity falls by 67 to 94% where all five perspectives pool at every round, and the one topology that never pools them is the one it cannot reliably repair. Medical multi-agent systems do not filter demographic bias; they launder it into plausible decisions no single-version audit can catch, and the only defense is to make the bias visible.

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