Although most undergraduates now use large language models (LLMs), a form of generative artificial intelligence (GenAI) for academic writing, no validated method distinguishes the qualitatively different ways students rely on them. Existing instruments assess reliance solely by frequency of use, a measure that, as this study shows, inadvertently rewards dependence on AI rather than recognizing students' own intellectual contribution. Conducted at a public minority-serving university and grounded in the AI Literacy Framework, Expectancy-Value Theory, and Biggs's Presage-Process-Product model, the study drew on 382 undergraduates, 14 interviews, and 396 open-ended survey responses. Four distinct reliance types were identified and confirmed: Strategic (34.3%), Instrumental (30.9%), Dialogic (30.4%), and Dependent (4.5%). Students' value and cost beliefs predicted the intensity of their reliance on LLMs, whereas their AI literacy predicted the type of reliance they adopted, indicating that differentiated support is needed. Notably, Strategic users, those who engaged AI most deliberately, scored lowest on standard outcome measures. This pattern reflects a limitation of current instruments, which index AI's contribution rather than writing quality, thereby penalizing students who show the greatest independent thinking. Analysis also revealed an additional group, roughly 13%, who declined to use AI for ethical rather than practical reasons, and who existing frameworks overlook. These findings carry implications for AI literacy programs, the measurement of student learning outcomes, and equitable AI policy at minority-serving institutions.

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