Cognitive trust and the belief that a robot is capable of accurately performing tasks, are recognized as central factors in fostering high-quality human-robot interactions. It is well established that performance factors such as the robot's competence and its reliability shape cognitive trust. Recent studies suggest that affective factors, such as robotic attentiveness, also play a role in building cognitive trust. This work explores the interplay between these two factors that shape cognitive trust. Specifically, we evaluated whether different combinations of robotic competence and attentiveness introduce a compensatory mechanism, where one factor compensates for the lack of the other. In the experiment, participants performed a search task with a robotic dog in a 2x2 experimental design that included two factors: competence (high or low) and attentiveness (high or low). The results revealed that high attentiveness can compensate for low competence. Participants who collaborated with a highly attentive robot that performed poorly reported trust levels comparable to those working with a highly competent robot. When the robot did not demonstrate attentiveness, low competence resulted in a substantial decrease in cognitive trust. The findings indicate that building cognitive trust in human-robot interaction may be more complex than previously believed, involving emotional processes that are typically overlooked. We highlight an affective compensatory mechanism that adds a layer to consider alongside traditional competence-based models of cognitive trust.