As Artificial Intelligence (AI) is increasingly promoted and used in qualitative research, it also raises profound methodological issues. This position paper critically interrogates the role of generative AI (genAI) in the context of qualitative coding methodologies. Despite widespread hype and claims of efficiency, we propose that genAI is not methodologically valid within qualitative inquiries, and its use risks undermining the robustness and trustworthiness of qualitative research. The lack of meaningful documentation, commercial opacity, and the inherent tendencies of genAI systems to produce incorrect outputs all contribute to weakening methodological rigor. Overall, the balance between risk and benefits does not support the use of genAI in qualitative research, and our position paper cautions researchers to put sound methodology before technological novelty.