Data consistency between unstructured clinical notes and structured tables in Electronic Health Records (EHRs) is essential for patient safety and clinical decision-making. However, existing work on note-table consistency verification mainly relies on surface-level matching of numeric values or simple events. Such approaches fail to capture the reasoning underlying real-world EHR documentation, including clinical interpretation, event relations, and temporal changes. To address this gap, we introduce EHR-ReasonCon, a reasoning-intensive benchmark for note-table consistency verification. Built on MIMIC-III with expert-guided annotations, it comprises 8,048 entities derived from clinical notes and provides high-quality ground-truth labels. The annotation protocol is supported by specialized table-exploration tools to ensure systematic evidence retrieval and reliable consistency assessment. We also propose EHR-Inspector, an LLM-based framework that segments notes, extracts anchor entities and temporal references, and uses table-exploration tools to verify consistency against structured tables. Evaluated using expert-validated LLM-as-a-judge metrics under harsh and lenient criteria, EHR-Inspector achieves state-of-the-art performance across multiple model backbones. Analyses further demonstrate the effectiveness of its components and highlight differences from human verification.