Large language models (LLMs) often achieve impressive predictive accuracy, yet correctness alone does not imply genuine understanding. True LLM understanding, analogous to human expertise, requires making consistent, well-founded decisions across multiple instances and diverse domains, relying on relevant and domain-grounded decision factors. We introduce Structured Tabular Decision Simulations (STaDS), a suite of expert-like decision settings that evaluate LLMs as if they were professionals undertaking structured decision ``exams''. In this context, understanding is defined as the ability to identify and rely on the correct decision factors, features that determine outcomes within a domain. STaDS jointly assesses understanding through: (i) question and instruction comprehension, (ii) knowledge-based prediction, and (iii) reliance on relevant decision factors. By analyzing 9 frontier LLMs across 15 diverse decision settings, we find that (a) most models struggle to achieve consistently strong accuracy across diverse domains; (b) models can be accurate yet globally unfaithful, and there are frequent mismatches between stated rationales and factors driving predictions. Our findings highlight the need for global-level understanding evaluation protocols and advocate for novel frameworks that go beyond accuracy to enhance LLMs' understanding ability.