Outpatient referral (OR) is a core clinical workflow that assigns patients to hospital departments under incomplete and evolving information, yet it is commonly simplified as a static classification problem despite being inherently interactive in practice. In this work, we study outpatient referral as a dynamic process driven by information acquisition and uncertainty reduction. We analyze both static scenarios based on fixed patient information and dynamic scenarios involving multi-turn dialogue, to test whether large language models (LLMs) improve referral outcomes through better prediction or more effective questioning. Our findings show that LLMs offer limited advantages over traditional classifiers in static referral accuracy, but consistently outperform them in dynamic settings by asking discriminative follow-up questions that reduce uncertainty over candidate departments. These results suggest that the primary value of LLMs in outpatient referral lies not in static prediction, but in supporting interactive, uncertainty-aware clinical decision-making.