This study examines how students integrate generative artificial intelligence (AI) into design projects through the lens of the SuperSkillsStack framework, which identifies four key human competencies for effective human-AI collaboration: Agency, Domain Knowledge, Imagination, and Taste. As generative AI increasingly transforms creative practice, design education must consider how human capabilities are cultivated alongside technological tools. Using qualitative thematic analysis, this study analyzes reflective writings from 80 student design teams participating in a human-centered design course. The findings show that students primarily used AI during the early stages of the design process, including brainstorming, information synthesis, and problem framing. However, students consistently relied on human judgment to interpret contextual information, validate AI-generated outputs, and refine design solutions. Domain knowledge derived from field observations enabled students to detect inaccuracies in AI suggestions, while taste played a critical role in evaluating and selecting meaningful ideas. The results suggest that generative AI functions primarily as a cognitive accelerator rather than a replacement for human creativity. The study highlights the importance of cultivating higher-order human capabilities to support effective human-AI collaboration in design education.