The rapid proliferation of Internet of Things (IoT) devices in critical healthcare infrastructure has introduced significant security and privacy challenges that demand innovative, distributed architectural solutions. This paper proposes FE-ACS (Fog-Edge Adaptive Cybersecurity System), a novel hierarchical security framework that intelligently distributes AI-powered anomaly detection algorithms across edge, fog, and cloud layers to optimize security efficacy, latency, and privacy. Our comprehensive evaluation demonstrates that FE-ACS achieves superior detection performance with an AUC-ROC of 0.985 and an F1-score of 0.923, while maintaining significantly lower end-to-end latency (18.7 ms) compared to cloud-centric (152.3 ms) and fog-only (34.5 ms) architectures. The system exhibits exceptional scalability, supporting up to 38,000 devices with logarithmic performance degradation—a $67\times$ improvement over conventional cloud-based approaches. By incorporating differential privacy mechanisms with balanced privacy-utility tradeoffs ( $\text{ε}=1.0$–1.5), FE-ACS maintains 90%–93% detection accuracy while ensuring strong privacy guarantees for sensitive healthcare data. Computational efficiency analysis reveals that our architecture achieves a detection rate of 12,400 events per second with only 12.3 mJ energy consumption per inference. In healthcare risk assessment, FE-ACS demonstrates robust operational viability with low patient safety risk (14.7%) and high system reliability (94.0%). The proposed framework represents a significant advancement in distributed security architectures, offering a scalable, privacy-preserving, and real-time solution for protecting healthcare IoT ecosystems against evolving cyber threats.