This article introduces a formal study on access-unrestricted data anonymity. It includes four aspects: (1) analyzes the impacts of anonymity on data usability; (2) quantitatively measures privacy disclosure risks in practical environment; (3) discusses the factors resulting in privacy disclosure; and (4) proposes the improved anonymity solutions within typical k-anonymity model, which can effectively prevent privacy disclosure that is related with the published data properties, anonymity principles, and anonymization rules. With the experiments, the authors have proven the existence of these potential privacy inference violations as well as the enhanced privacy effect by the new anti-inference policies for access-unrestricted data publication.