The AI community has shown substantial interest in the concept of world models: internal representations that simulate aspects of the external world, track entities and states, capture causal relationships, and enable prediction of consequences. This contrasts with representations based solely on statistical correlations. A key motivation behind this research direction is the argument that humans possess such mental world models, and finding evidence of similar representations in AI models might indicate that these models truly "understand" the world in a human-like way. In this paper, we use problems and case studies from the philosophy of science literature to critically examine whether the world model framework adequately characterizes human-level understanding. We focus on specific philosophical analyses where the distinction between world model capabilities and human understanding is most pronounced. While these represent particular views of understanding rather than universal definitions, they illuminate some important limitations in using world models as a lens to claim that AI models understand in a human-like way. By highlighting these distinctions, we hope to stimulate deeper discussion about the nature of understanding in both human and artificial contexts.