The scale and scope of online education increasingly expand. In tandem, interest grows among educators and scholars in understanding the personal and contextual factors that moderate the efficient design and effective delivery of an online course. This paper looks at a theoretically robust method, peer assessment administered by the Canvas learning management system, and evaluates its potential and performance in university-level hybrid and online courses. Cross-sectional data profile students' views, both prior to as well as post-experience, of aspects of the peer review process. Frequency analyses, mean comparisons, and t-tests highlight students' initial strong, positive agreement with the potential but then, post-experience, weaker support of the value of peer assessment. Controlling for time and place, in terms of hybrid versus online sections, did not moderate this outcome. Collectively, these results call for refining our interpretation of the utility of peer assessment to promoting student engagement. We evaluate the moderating influence of anonymity and the social dynamic of self-directed learning, particularly given the implications of the "anytime, anyplace" instrumentality of online education. We close with a series of pedagogical recommendations.