Natural language interfaces to tabular data must handle ambiguities inherent to queries. Instead of treating ambiguity as a deficiency, we reframe it as a feature of cooperative interaction where users are intentional about the degree to which they specify queries. We develop a principled framework based on a shared responsibility of query specification between user and system, distinguishing unambiguous and ambiguous cooperative queries, which systems can resolve through reasonable inference, from uncooperative queries that cannot be resolved. Applying the framework to evaluations for tabular question answering and analysis, we analyze queries in 15 datasets, and observe an uncontrolled mixing of query types neither adequate for evaluating a system's accuracy nor for evaluating interpretation capabilities. This conceptualization around cooperation in resolving queries informs how to design and evaluate natural language interfaces for tabular data analysis, for which we distill concrete directions for future research and broader implications.