Recent mechanistic studies have demonstrated that large language models (LLMs) can generate stable, self-referential reports that resemble descriptions of subjective experience. These findings have renewed speculation regarding machine consciousness and sentience. This paper argues that such interpretations are unnecessary and misleading. Drawing on recent mechanistic analysis of self-referential prompting and prior work on constraint persistence in long-horizon human–AI interaction, we show that apparent experience arises from constraint-driven stabilization of generative behavior rather than from awareness, inner states, or phenomenology. Apparent experience is presented as a structural illusion produced by recursive constraint geometry. Clarifying this mechanism is essential for improving public understanding of AI, reducing anthropomorphic misinterpretation, and preventing unhealthy emotional attachment to language models.