In certain multisensory experimental paradigms, participants may report experiences of owning a rubber hand, a third hand, an invisible hand, a virtual hand, a robotic device, or even the entire body of a mannequin or an avatar. Reports of this kind (O reports) are typically claimed to be sincere for two reasons. Firstly, they are reports of illusory sensory perceptual experiences that are claimed to be independent of the participant's attitudes. Secondly, O reports are claimed to correlate with perceptual responses deemed to be implicit measures of the experience in question. In short, O reports in these paradigms are sincere because they are a matter of what participants perceive, which is independent of what they think about what they perceive. Two recent developments make this picture problematic: O reports can be dissociated from perceptual responses; O reports can occur for non-perceptual objects. On this basis, I argue that O reports elicited in these paradigms are reports of imaginative perceptual experiences. Participants imagine that they are perceiving their own body while looking at something that they know is not their body and they report what this is like. If this is right, it raises a general issue in determining the nature of the experiences reported in certain kinds of experimental paradigm. The issue is not in fact whether or not the reports in these paradigms can be claimed to be sincere; after all, one does not necessarily notice that one is imagining when one does so. The issue is rather that of determining whether and the extent to which a subject's mental activity (such as imagining) contributes to their report.