Logical Table-to-Text (LT2T) generation aims to produce natural-language sentences that are logically faithful to structured tabular data. While recent Large Language Models (LLMs) show high performance on aggregate fidelity metrics, these scores provide only a coarse view of performance, obscuring specific logic-type reasoning failures and models’ meta-logical awareness. We propose an operation-aware diagnostic framework that evaluates four core competencies: (1) Logical Form (LF) execution accuracy, (2) fidelity of LF-conditioned generation, (3) logic-type identification, and (4) LF-free generation.We apply this framework to a suite of frontier LLMs and perform fine-grained analysis across logic types such as aggregation, ordinal, and superlative reasoning. Our results show that LT2T fidelity assessment can be unstable; the choice of verifier and logic type can substantially alter conclusions and model rankings. Crucially, we identify a meta-logical gap: models often generate faithful statements while failing to identify the underlying operation.