Knee osteoarthritis (OA) assessment involves a natural but often underused label hierarchy: a coarse binary OA decision and a fine-grained Kellgren--Lawrence (KL) severity grade. Existing deep learning studies commonly treat these targets as separate classification problems, either reducing OA assessment to disease presence or directly optimizing noisy ordinal KL labels. In this work, we ask whether this clinical hierarchy can serve as a representation-level supervisory prior. Rather than introducing a complex architecture, we use a deliberately simple dual-head model with a shared encoder and two task-specific heads as a probe of hierarchical supervision. We compare single-OA, single-KL, and dual-head training across multiple 3D backbones under the same test protocol. Beyond standard classification metrics, we perform paired statistical comparisons, analyze latent severity-axis geometry, and examine saliency overlap with cartilage regions. The results show that dual-head supervision produces backbone-dependent gains, with clear improvements in KL-related metrics for selected backbones. More importantly, the gains are accompanied by a more ordered coarse-to-fine latent organization and, for responsive backbones, stronger anatomical alignment of saliency with cartilage. These findings suggest that even simple hierarchical dual-head supervision can reshape disease representations under noisy coarse/fine labels, providing a useful inductive bias for OA diagnosis and severity grading.