According to the Cue integration theory, the Sense of agency (SoA) is a resultant of both motor as well as non-motor cues, and these multiple cues are integrated based on their reliability or invariance estimate. However, the cue integration theory fails to make a distinction between perception and judgment, when it attributes (multisensory) perceptual character to non-motor cues like affect, effort, competition, fluency, familiarity, expertise, sleep, meditation, primes, and previews of actions, etc. Thus, my paper criticizes the experimentally operationalized cue-integrated SoA by arguing that: (a) there is uncertainty in the cue-integrated SoA experimental operationalization (making the participants prone to judgment effects); (b) the cue integration theory faces a problem of explaining how non-motor cues acquire interface, intentionality, and accuracy about agency; (c) the SoA reports are influenced by heuristic responding pattern (under uncertainty); (d) the cue-integrated SoA operationalizations had ‘inaccuracy standard’ for measuring perception of agency; (e) under certainty, the (nonveridical) SoA reports might not have occurred at all. This paper concludes that the reported heuristic responses (under uncertainty) of SoA can be parsimoniously accounted by compositionality nature of thought/judgment rather than the cue-integrated perception, and thus, the cue-integrated SoA reports are not instances of perceptions but are judgments.