Frontier large language models generate clinically accurate outputs, but their citations are often fabricated. We term this the Provenance Gap. We tested five frontier LLMs across 36 clinician-validated scenarios for three rare neuromuscular disease pairs. No model produced a clinically relevant PubMed identifier without prompting. When explicitly asked to cite, the best model achieved 15.3% relevant PMIDs; the majority resolved to real publications in unrelated fields. We present HEG-TKG (Hierarchical Evidence-Grounded Temporal Knowledge Graphs), a system that grounds clinical claims in temporal knowledge graphs built from 4,512 PubMed records and curated sources with quality-tier stratification and 1,280 disease-trajectory milestones. In a controlled three-arm comparison using the same synthesis model, HEG-TKG matches baseline clinical feature coverage while achieving 100% evidence verifiability with 203 inline citations. Guideline-RAG, given overlapping source documents as raw text, produces zero verifiable citations. LLM judges cannot distinguish fabricated from verified citations without PubMed audit data. Independent clinician evaluation confirms the verifiability advantage (Cohen's d = 1.81, p < 0.001) with no degradation on safety or completeness. A counterfactual experiment shows 80% resistance to injected clinical errors with 100% detectability via citation trace. The system deploys on-premise via open-source models so patient data never leaves institutional infrastructure.