Existing tabular reasoning benchmarks typically assume that input tables are clean and error-free, which contrasts sharply with real-world data pipelines where noise and anomalies are pervasive. While humans routinely validate tables and reject conclusions when anomalies render a question unanswerable, it remains unclear whether large language models (LLMs) exhibit similar anomaly awareness. In this work, we introduce AnTBench, a benchmark designed to systematically evaluate LLM behavior under anomalous tabular data. AnTBench consists of 1,571 curated instances covering five common and verifiable anomaly types. Experiments on 14 representative LLMs reveal a pronounced capability–behavior gap: even the strongest model achieves 76.07% on explicit anomaly detection, yet only 19.03% on spontaneous anomaly perception during standard table QA. As an inference-time mitigation, we introduce the Multi-Path Thinker, a multi-path reasoning framework. While this approach improves explicit anomaly detection, enforcing proactive verification for every query is practically prohibitive. We urge the community to move beyond inference-time patches and instill spontaneous anomaly awareness directly into the training and alignment phases. Our code and data are available at https://github.com/Wei12097/AnTBench.