This study investigated how accurate and inaccurate information attributed to artificial intelligence (AI) might be associated with humans’ cognitive reactions. Tracing the literature on the machine heuristic, this study used an experiment with a 2 (Agent: human vs. AI) × 2 (Information Veracity: accurate vs. inaccurate) design to test how endorsement of the machine heuristic relates to evaluations of factual claims. Participants rated identical short messages embedded in either an AI news bot profile or a human journalist profile, and then evaluated source credibility, perceived objectivity, perceived bias, and perceived accuracy. Endorsement of the machine heuristic was significantly associated with higher source credibility, perceived objectivity, and perceived accuracy, and lower perceived bias, whereas agent type and information veracity showed no significant effects in the full sample. In post hoc analyses, differences by agent and information veracity emerged only among participants high in the machine heuristic. These findings suggest boundary conditions of the machine heuristic: while it shapes perceptions, its operation appears increasingly agnostic to human versus AI source cues. We call this the evanishing effect, wherein source cues (human vs. AI) are recognized but do not systematically alter evaluations, so neither human nor machine agents are consistently preferred. This pattern supports interpreting the machine heuristic as an individual difference rather than a uniformly cue-dependent response.