General-purpose AI models have emerged as a disruptive technology with paramount spillover economic effects across industries. The owners of such models, namely big tech enterprises, can leverage their dominance in general-purpose AI models to expand into existing or new downstream markets. However, competition law is poised to constrain this expansion effectively. Nevertheless, there is uncertainty about the legal standard when assessing a refusal to deal in the case of access to general-purpose AI models. While EU competition law judicial practice reveals an adversary tendency against big tech enterprises leveraging in downstream markets, there is a case for adopting a narrower standard regarding access to general-purpose AI models.