Dysarthria severity assessment is essential for therapy planning and longitudinal monitoring, yet manual perceptual rating is time-consuming and variable across clinicians. Although deep learning models achieve strong performance, their black-box nature limits clinical adoption. Existing speech explainability methods typically provide acoustic feature importance scores that are difficult for end-users to interpret. We propose an influence-based, instance-level explainability framework that explains each decision through supportive and competing training samples. Using gradient-based influence approximations, we compute per-utterance influence scores to identify supportive and competing training samples for each prediction. Controlled deletion experiments from 5 to 20 percent validate the explanations, showing that removing highly influential samples systematically shifts predictions. This approach provides auditable explanations by linking decisions to perceptible reference cases.