Pixel-level annotation is costly in low-resource dermoscopy. We present RABC-Net, a reliability-aware annotation-free segmentation system that combines pseudo-label reliability learning, restricted target-domain adaptation, and Reliability-Adaptive Boundary Calibration (RABC). The system decouples reliability learning from deployment: uncertainty-aware pseudo-label interaction shapes robust representations during training, while the image-only inference path is preserved and RABC performs local logit-space calibration from boundary confidence, uncertainty, and foreground probability. No manual masks are used for training or target-domain adaptation; validation labels, when available, are used only for final operating-point selection. Across ISIC-2017, ISIC-2018, and PH2, RABC-Net achieves macro-average DICE/JAC of 86.58\%/79.47\% and consistent matched-protocol results. Controlled within-study analyses show that RABC provides localized gains over nonlearned boundary correction, while the overall result comes from the full reliability-aware system. Adaptation updates only 3.50\% of model parameters, image-only inference runs at 87.4 FPS, and the selected operating points use $σ=0$ on all three datasets, indicating that learned calibration avoids extra smoothing at deployment.