The integration of artificial intelligence (AI) into healthcare requires preparing professionals to engage critically with intelligent systems. Moving beyond isolated predictors, this study investigates a multi-layered psychological model of AI acceptance, drawing on Self-Determination Theory (SDT), and proposes a psychologically grounded model in which the satisfaction of basic psychological needs serves as a proximal mechanism shaping attitudes toward AI. A cross-sectional survey was conducted with 233 Italian healthcare students and professionals. Participants completed validated measures of attitudes toward AI, psychological need satisfaction in relation to technology (autonomy, competence, relatedness), personality traits (Big Five and Dark Triad), conspiracy beliefs, and AI literacy. Hierarchical regression analyses were used to test the incremental contribution of motivational, dispositional, and cognitive factors. Additionally, comparative evaluations were conducted to assess the perceived competence of AI versus human professionals across different clinical domains. The final models explained a substantial proportion of the variance in both positive and negative attitudes. SDT variables provided strong incremental validity, emerging as the primary factors in promoting AI acceptance and mitigating AI aversion. Regarding comparative competence, AI was perceived as outperforming humans in system-level and analytical tasks, but significantly less skilled in domains requiring psychological and relational support. Findings support a theory-driven account of AI acceptance in healthcare education, highlighting psychological need satisfaction as a key mechanism by which individuals evaluate emerging technologies. This extends SDT to the domain of human–AI interaction, suggesting that acceptance depends not only on knowledge or exposure, but on whether engagement with AI supports autonomy, competence, and relatedness. AI training fostering a meaningful and responsible integration of AI in healthcare should move beyond technical instruction to include participatory, competence-building, and reflective approaches that address learners’ motivational needs.