Money laundering threatens financial stability and exposes institutions to penalties, motivating automated detection. Because laundering schemes often emerge through relational patterns, graph neural networks (GNNs) are increasingly used for anti-money laundering (AML). Yet AML GNNs are typically evaluated with aggregate metrics such as overall F1 score, which hide an operational issue: high-activity recipient accounts concentrate many incoming transactions, making suspicious signals harder to isolate and costlier to investigate. We introduce a recipient-degree stratified evaluation that reports standard AML metrics across recipient-context density. Across three datasets (HI-Small, HI-Medium, and AMLSim-32k-5%), it reveals consistent degradation in dense recipient contexts, which we trace to three GNN characteristics: two known limitations that AML amplifies, i.e., (1) multiset non-discriminability and (2) cardinality blindness, and (3) an attention-specific effect: in dense neighborhoods, normalized attention attenuates weak but pattern-relevant multi-hop signals. Guided by this diagnosis, we propose SALT-GNN, a lightweight statistics-aware architecture that fuses degree-aware statistical aggregation with attention at each message-passing layer, so distributional and cardinality information shapes the node states used by subsequent attention steps. Ablations support fusion placement as a key factor in dense-context performance. On HI-Small and HI-Medium, SALT-GNN uses up to 77% fewer parameters than task-specific graph-transformer baselines while improving dense-context F1 score by 3-6 points; on AMLSim-32k-5%, it improves highest-degree F1 score by 16-20 points. The gains hold for both Transformer- and GAT-style attention, indicating that the benefit comes from where statistical and attentional evidence is fused rather than from a specific attention operator.

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