The widespread availability of generative artificial intelligence (GenAI) has created a pressing challenge in computer science (CS) education: how to incorporate powerful AI tools into programming coursework without undermining student learning through cognitive offloading. This paper presents an assessment model that permits the use of generative AI for take-home programming assignments while enforcing individual mastery through immediate, assignment-driven written quizzes. To promote authentic learning, these in-class, closed-book assessments are weighted more heavily than the assignments themselves and are specifically designed to verify the student's comprehension of the algorithms, structure, and implementation details of their submitted code. Preliminary empirical data were collected from an upper-level computer science course to examine the relationship between self-reported GenAI usage and performance on AI-free quizzes, exams, and final course grades. Statistical analyses revealed no meaningful linear correlation between GenAI usage levels and assessment outcomes, with Pearson correlation coefficients consistently near zero. These preliminary results suggest that allowing GenAI for programming assignments does not diminish students' mastery of course concepts when learning is verified through targeted, assignment-driven quizzes. Although limited by a small sample size, this study provides preliminary evidence that the risks of cognitive offloading can be mitigated by allowing AI-assisted programming practice while verifying understanding through assignment-driven, AI-free quizzes. The findings support the responsible adoption of open GenAI policies in upper-level CS courses, when paired with rigorous, independent assessment mechanisms.