Retrieval-Augmented Generation (RAG) reduces hallucinations by grounding answers in retrieved evidence, yet standard retrievers often exhibit retrieval sycophancy: they preferentially surface evidence that supports a user's premise, even when the premise is false. We propose FVA-RAG (Falsification-Verification Alignment RAG), a pipeline that inverts the standard RAG workflow by treating the initial response as a draft hypothesis and explicitly retrieving anti-context to stress-test it. We evaluate on the full TruthfulQA-Generation benchmark (N=817) under a fully frozen protocol with 0 live web calls and identical retrieval budgets across methods. Using gpt-4o for generation and deterministic judging, FVA-RAG achieves 79.80-80.05% accuracy across two independently built frozen corpora , significantly outperforming prompted variants of Self-RAG (71.11-72.22%) and CRAG (71.36-73.93%) with p < 10^-6 according to McNemar's test. FVA-RAG triggers falsification on 24.5-29.3% of queries, demonstrating that targeted counter-evidence retrieval is decisive for mitigating premise-confirming hallucinations.