There is a growing concern that generative AI models may generate outputs that closely resemble the copyrighted input content used for their training. This worry has intensified as the quality and complexity of generative models have immensely improved, and the availability of extensive datasets containing copyrighted material has expanded. Researchers are actively exploring strategies to mitigate the risk of producing infringing samples, and a recent line of work suggests employing techniques such as differential privacy and other forms of algorithmic stability to safeguard copyrighted content.In this work, we examine whether algorithmic stability techniques such as differential privacy are suitable to ensure the responsible use of generative models without inadvertently violating copyright laws. We argue that there are fundamental differences between privacy and copyright that should not be overlooked. In particular, we highlight that although algorithmic stability may be perceived as a practical tool to detect copying, it does not necessarily equate to copyright protection. Therefore, if it is adopted as a standard for copyright infringement, it may undermine the intended purposes of copyright law