The debate around the interpretability of attention mechanisms is centered on whether attention scores can be used as a proxy for the relative amounts of signal carried by sub-components of data. We propose to study the interpretability of attention in the context of set machine learning, where each data point is composed of an unordered collection of instances with a global label. For classical multiple-instance-learning problems and simple extensions, there is a well-defined “importance” ground truth that can be leveraged to cast interpretation as a binary classification problem, which we can quantitatively evaluate. By building synthetic datasets over several data modalities, we perform a systematic assessment of attention-based interpretations. We find that attention distributions are indeed often reflective of the relative importance of individual instances, but that silent failures happen where a model will have high classification performance but attention patterns that do not align with expectations. Based on these observations, we propose to use ensembling to minimize the risk of misleading attention-based explanations.