Despite the growing availability of high-quality public datasets, the lack of training samples is still one of the main challenges of deep-learning for skin lesion analysis. Generative Adversarial Networks (GANs) appear as an enticing alternative to alleviate the issue, by synthesizing samples indistinguishable from real images, with a plethora of works employing them for medical applications. Nevertheless, carefully designed experiments for skin-lesion diagnosis with GAN-based data augmentation show favorable results only on out-of-distribution test sets. For GAN-based data anonymization $-$ where the synthetic images replace the real ones $-$ favorable results also only appear for out-of-distribution test sets. Because of the costs and risks associated with GAN usage, those results suggest caution in their adoption for medical applications.