Enterprise AI assistants must produce responses that are verifiable and traceable to source evidence. However, retrieval-augmented generation (RAG) over heterogeneous enterprise data can suffer from citation drift, unsupported content, and weak source traceability. We present EvidenT (T = Trust + Transparency + Traceability), a lightweight pipeline that verifies extracted evidence against retrieved documents before answer generation, without model retraining. EvidenT combines structured passage extraction with deterministic lexical alignment to filter unsupported content, correct citation drift, and preserve source-span traceability. On approximately 500 real enterprise queries, EvidenT improves gold-source hit rate by an average of 29% over prompting baselines, produces no citations to non-retrieved urls, and achieves near-saturated answer-to-source lexical coverage.