Generative AIs have been embraced by learners wishing to offload (parts of) complex tasks. However, recent research suggests that AI users are at risk of failing to correctly monitor the extent of their own contribution when being assisted by an AI. This difficulty in keeping track of the division of labor has been shown to result in placebo and ghostwriter effects. In case of the AI-based placebo effect, users overestimate their ability while or after being assisted by an AI. The ghostwriter effect occurs when AI users do not disclose their AI use despite being aware of the contribution made by an AI. These two troubling effects are discussed in the context of the conflict between cognitive externalization and anthropomorphization. While people tend to offload cognitive load into their environment, they also often perceive technology as human-like. However, despite the natural conversations that can be had with current AIs, the desire to attribute human-like qualities that would require the acknowledgment of AI contributions appears to be lacking. Implications and suggestions on how to improve AI use, for example, by employing embodied AI agents, are discussed.