As Automatic Speech Recognition (ASR) is increasingly deployed in clinical dialogue, standard evaluations still rely heavily on Word Error Rate (WER). This paper challenges that standard, investigating whether WER or other common metrics correlate with the clinical impact of transcription errors. We establish a gold-standard benchmark by having expert clinicians compare ground-truth utterances to their ASR-generated counterparts, labeling the clinical impact of any discrepancies found in two distinct doctor-patient dialogue datasets. Our analysis reveals that WER and a comprehensive suite of existing metrics correlate poorly with the clinician-assigned risk labels (No, Minimal, or Significant Impact). To bridge this evaluation gap, we introduce an LLM-as-a-Judge, programmatically optimized using GEPA through DSPy to replicate expert clinical assessment. The optimized judge (Gemini-2.5-Pro) achieves human-comparable performance, obtaining 90% accuracy and a strong Cohen's kappa of 0.816. This work provides a validated, automated framework for moving ASR evaluation beyond simple textual fidelity to a necessary, scalable assessment of safety in clinical dialogue.