Current state-of-the-art multi-class unsupervised anomaly detection (MUAD) methods rely on training encoder--decoder models to reconstruct anomaly-free features. However, we argue that such task-specific training is costly under distribution shifts, and that reconstruction-based residual scoring further faces a fidelity--stability dilemma. Existing training-free alternatives, in turn, remain prone to cross-category and cross-region mismatches in MUAD. Motivated by these limitations, we propose Retrieval-based Anomaly Detection (RAD), a task-specific training-free framework that stores anomaly-free features in a memory and detects anomalies through multi-level retrieval, matching test patches against the memory. Experiments demonstrate that RAD achieves state-of-the-art performance across four established benchmarks (MVTec-AD, VisA, Real-IAD, 3D-ADAM) under both standard and few-shot settings. On MVTec-AD, RAD reaches 96.7% Pixel AUROC with just a single anomaly-free image compared to 98.5% of RAD's full-data performance. Collectively, these findings overturn the assumption that MUAD requires task-specific training, showing that state-of-the-art anomaly detection is feasible with training-free memory-based retrieval. Our code is available at https://github.com/longkukuhi/RAD.