Foundation models for medical image segmentation, like prompt-based MedSAM, generalize well across domains and modalities, often in zero or few-shot setups. However, their performance depends on the quality of prompts and the adaptation of the models to custom datasets. This work systematically examines how MedSAM generalizes across diverse medical imaging benchmarks, with six adaptation strategies: full-model and encoder-only LoRA, shallow and deep visual prompt tuning (VPT), and decoder-only and full fine-tuning. Models are trained on the International Skin Imaging Collaboration Challenge (ISIC 2018) dataset and evaluated under clean and increasingly noisy prompts on IN and Out-of-Distribution (OOD) datasets: close-OOD PH2 (dermoscopy), far-OOD BUSI (Breast Ultrasound Images Dataset) and CBIS-DDSM (Curated Breast Imaging Subset of the Digital Database for Screening Mammography). We show that adaptation improves performance on IN and close-OOD data but often reduces performance on far-OOD data. Full fine-tuning provides the best tradeoff, while encoder-only LoRA is the strongest parameter-efficient alternative, outperforming standard LoRA and VPT under far-OOD shifts. Using Centered Kernel Alignment (CKA), we show that far-OOD degradation is strongly associated with drift in decoder representations, whereas encoder similarity alone does not explain robustness. This suggests encoder-only LoRA provides stronger robustness than standard LoRA by adapting the encoder to distribution shift in visual features, while preserving the decoder pathway. We further show that random 0-100 pixel jitter on prompts produces more robust and better performing models. We thus conclude that robust MedSAM adaptation requires the combined consideration of prompt noise exposure, domain shift, and representation preservation. We release our code: https://github.com/ImSounic/medsam-vpt

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