Retrieval-Augmented Generation (RAG) enhances large language models with external evidence, but in compliance-oriented QA, semantic relevance alone does not determine whether evidence should be used for generation. A retrieved document may be relevant and factually correct, yet inadmissible because it is inaccessible to the current user, explicitly superseded, or in unresolved conflict with other active evidence. We formalize three post-retrieval governance failures in this setting: unauthorized leakage, stale citation, and unsupported answers. To address them, we propose TrustRAG, a RAG framework that incorporates a metadata-governed routing layer between the retriever and the generator. Given correct and complete governance metadata for the retrieved candidate set, this layer filters inadmissible evidence before generation, returns a deterministic refusal when no admissible evidence remains, and preserves unresolved conflicts for conflict-reporting generation. We construct AeroTrustBench, a counterfactual compliance QA benchmark for evaluating evidence governance in RAG. Across Qwen-Max, DeepSeek-V3, and GLM-4-32B-0414, TrustRAG consistently reduces the three failures relative to unguided RAG and baselines based on prompting, filtering, routing, verification, and recency. Mechanism-matched and 50-document comparisons show benefits beyond filtering under larger candidate pools, while metadata-noise tests and human audits characterize dependencies on upstream metadata and evaluator choice.