As Text-to-Image (T2I) generation becomes widespread, third-party platforms increasingly integrate multiple model APIs for convenient image creation. However, false claims of using official models can mislead users and harm model owners' reputations, making model verification essential to confirm whether an API's underlying model matches its claim. Existing methods address this by using verification prompts generated by official model owners, but the generation relies on multiple reference models for optimization, leading to high computational cost and sensitivity to model selection. To address this problem, we propose a reference-free T2I model verification method called Boundary-aware Prompt Optimization (BPO). It directly explores the intrinsic characteristics of the target model. The key insight is that although different T2I models produce similar outputs for normal prompts, their semantic boundaries in the embedding space (transition zones between two concepts such as "corgi" and "bagel") are distinct. Prompts near these boundaries generate unstable outputs (e.g., sometimes a corgi and sometimes a bagel) on the target model but remain stable on other models. By identifying such boundary-adjacent prompts, BPO captures model-specific behaviors that serve as reliable verification cues for distinguishing T2I models. Experiments on five T2I models and four baselines demonstrate that BPO achieves superior verification accuracy.