Trust is praised by many social scientists as the foundation of functioning social systems owing to its assumed connection to cooperative behavior. The existence of such a link is still subject to debate. In the present study, we first highlight important conceptual issues within this debate. Second, we examine previous evidence, highlighting several issues. Third, we present findings from an original experiment, in which we tried to identify a "real" situation that allowed us to measure both trust and cooperation. People's expectations and behavior when they decide to share (or not) their data represents such a situation, and we make use of corresponding data. We found that there is no relationship between trust and cooperation. This non-relationship may be rationalized in different ways which, in turn, provides important lessons for the study of the trust-behavior nexus beyond the particular situation we study empirically.