Differential privacy is one of the most popular technologies in the growing area of privacy-conscious data analytics. But differential privacy, along with other privacy-enhancing technologies, may enable privacy theater. In implementations of differential privacy, certain algorithm parameters control the tradeoff between privacy protection for individuals and utility for the data collector; thus, data collectors who do not provide transparency into these parameters may obscure the limited protection offered by their implementation. Through large-scale online surveys, we investigate whether explanations of differential privacy that hide important information about algorithm parameters persuade users to share more browser history data. Surprisingly, we find that the explanations have little effect on individuals' willingness to share data. In fact, most people make up their minds about whether to share before they even learn about the privacy protection.