Search agents reduce hallucination by grounding answers in retrieved web evidence. Yet reliance on retrieval also creates an attack surface: poisoned corpora with false or malicious documents can cause agents to reproduce misinformation. We show that falsehood is not necessary -- a search agent can be misled by factual evidence for a nearby question, adopting that nearby answer even when it does not answer the current question. We call this failure lazy grounding. We expose lazy grounding using nearby evidence from answer-changing rewrites of benchmark questions. Each document truthfully supports a neighboring rewritten question, but is surfaced for the original question. Across 12 model-benchmark pairs, nearby evidence reduces accuracy by 5.9 points on average and by up to 17.3 points, while inducing nearby-answer adoption in every setting. The effect is stronger when nearby evidence appears later or is more answer-shaped. Our results show that robust search agents must defend against not only misinformation but also the misapplication of factual evidence. The code is publicly available at https://github.com/frankyzha/lazy-grounding.

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