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Annotation-free skin lesion segmentation is attractive for low-resource dermoscopic deployment. However, its performance remains constrained by three coupled challenges: noisy pseudo-label supervision, unstable transfer under limited target-domain data, and boundary probability under-confidence. Most existing annotation-free methods primarily focus on pseudo-label denoising. In contrast, the effect of compressed boundary probabilities on final mask quality has received less explicit attention, although it directly affects contour completeness and cannot be adequately corrected by global threshold adjustment alone. To address this issue, we propose BPC-Net, a boundary probability calibration framework for annotation-free skin lesion segmentation. The core of the framework is Gaussian Probability Smoothing (GPS), which performs localized probability-space calibration before thresholding to recover under-confident lesion boundaries without inducing indiscriminate foreground expansion. To support this calibration under noisy pseudo-supervision and cross-domain transfer, we further incorporate two auxiliary designs: a feature-decoupled decoder that separately handles context suppression, detail recovery, and boundary refinement, and an interaction-branch adaptation strategy that updates only the pseudo-label interaction branch while preserving the deployed image-only segmentation path. Under a strictly annotation-free protocol, no manual masks are used during training or target-domain adaptation, and validation labels, when available, are used only for final operating-point selection. Experiments on ISIC-2017, ISIC-2018, and PH2 show that the proposed framework achieves state-of-the-art performance among published unsupervised methods, reaching a macro-average Dice coefficient and Jaccard index of 85.80\% and 76.97\%, respectively, while approaching supervised reference performance on PH2.