As large language models (LLMs) become default tools for online information verification, an implicit assumption follows them: that scale and general capability are sufficient for nuanced classification of misinformation discourse. We test this assumption directly on 900 Reddit comments spanning three PolitiFact-verified misinformation claims (environment, health, immigration), labelled as belief (propagates the claim), fact-check (corrects it), or other. We compare nine models across three paradigms -- BART-MNLI, three Llama variants, three commercial frontier LLMs (Claude Haiku 4.5, Gemini Flash Lite 2.5, Claude Sonnet 4.6), and fine-tuned DistilBERT and RoBERTa -- under universal and topic-specific label schemas. The assumption does not hold. Fine-tuned RoBERTa reaches 0.62 macro-$F_1$ against a best zero-shot result of 0.50 (Claude Haiku 4.5), at a fraction of the per-query cost; the supervised advantage is concentrated on the belief class, the implicit, affective category every zero-shot model under-detects. Scaling does not help: Llama-3-8B matches Llama-3-70B, and Claude Sonnet 4.6 underperforms the smaller Haiku under generic labels, collapsing belief detection to 0.17 and refusing outright on a subset of comments flagged as sensitive. This is a safety-alignment artefact, not a capacity limit. Label schema and topic jointly shape zero-shot performance, with the same model varying by more than 0.13 macro-$F_1$ across topics under matched labels. In a verification context, where missing belief is the costlier error, task-specific fine-tuning remains the more reliable choice despite the proliferation of large generative models.