Denial Constraints (DCs) are a flexible formalism to express many types of data rules, making them a widely adopted tool for many applications. This flexibility led to the development of numerous algorithms to automatically discover DCs directly from data. However, few studies have been conducted on the quality of the discovered DCs. We experimentally quantify the lack of quality in the results obtained by state-of-the-art algorithms, showing how the proportion of discovered DCs that are false is rarely below 95%. We hypothesize that the common source of these erroneous DCs stems from the adoption of the current DC validity definition. We use a statistical approach to explain the mechanism leading to these results, and propose a redefinition of DC validity properties to avoid the acceptance of false DCs. We validate this redefinition experimentally, showing that it exclusively accepts true constraints of the data, and is reliable enough to discover DCs missed by domain experts. Additionally, we provide curated sets of golden DCs for each dataset used in our study, those generated by domain experts and those discovered using our approach.