In this study, we present Healthcare Codec-Fake Detection (HCFD), a new task for detecting codec-fakes under pathological speech conditions. We intentionally focus on codec based synthetic speech in this work, since neural codec decoding forms a core building block in modern speech generation pipelines. First, we release Healthcare CodecFake, the first pathology-aware dataset containing paired real and NAC-synthesized speech across multipl clinical conditions and codec families. Our evaluations show that SOTA codec-fake detectors trained primarily on healthy speech perform poorly on Healthcare CodecFake, highlighting the need for HCFD-specific models. Second, we demonstrate that PaSST outperforms existing speech-based models for HCFD, benefiting from its patch-based spectro-temporal representation. Finally, we propose PHOENIX-Mamba, a geometry-aware framework that models codec-fakes as multiple self-discovered modes in hyperbolic space and achieves the strongest performance on HCFD across clinical conditions and codecs. Experiments on HCFK show that PHOENIX-Mamba (PaSST) achieves the best overall performance, reaching 97.04 Acc on E-Dep, 96.73 on E-Alz, and 96.57 on E-Dys, while maintaining strong results on Chinese with 94.41 (Dep), 94.40 (Alz), and 93.20 (Dys). This geometry-aware formulation enables self-discovered clustering of heterogeneous codec-fake modes in hyperbolic space, facilitating robust discrimination under pathological speech variability. PHOENIX-Mamba achieves topmost performance on the HCFD task across clinical conditions and codecs.