In medical LLM adaptation, collecting large-scale real clinical notes is constrained by patient privacy and annotation cost, so training pipelines often rely on notes synthesized by commercial LLMs. Those synthetic notes are not error-free. We observe that after fine-tuning on such notes, a task judge rates the resulting model’s outputs as more complete without a consistent Accuracy gain, while a hallucination judge flags more statements that the source does not support. We therefore report Accuracy and Completeness separately from hallucination counts, split the latter into Content and Format-Meta hallucinations, and report both as rates normalized by the number of fields each output format requires, so that a gain in one cannot hide a loss in the other. We then introduce Self-Detect–Refine, which applies an external LLM to detect and revise hallucinations in the training labels themselves rather than in outputs at inference time. We evaluate it across three base models, two refiners, and four refinement depths, fine-tuning a fresh copy of each base model on each label snapshot. GPT-5.2-refined labels lower Content hallucinations in every configuration, both as a share of the required fields and after length normalization. The two stages load on different components: the Completeness gain belongs to raw-label fine-tuning, whereas refinement raises Accuracy without a consistent loss in Completeness. Format-Meta changes are mixed, a lower-cost refiner is less consistent, and every judgment here comes from LLM judges on a single synthetic benchmark without clinician validation.