No. Stop pushing that utterly stupid statement. It has neither factual nor legal merit.
And yet you are wrong on both accounts, both in the physical analogy and in the legal sense.
a) An AI does not copy and store the original text, but rather trains a neural network with weights that represent the learned material. This is literally modelled on human learning processes and how our brains work, it's why the process was given the name in the first place, it's similar to how neurons work.
b) This has been definitively ruled on directly for the training process of the company in question by a different plaintiff: Bartz, et al. v. Anthropic PBC
"The court held that Anthropic’s use of copyrighted books for LLM training was “spectacularly” transformative and qualified as fair use. The training process involved analyzing statistical relationships between text fragments to enable the LLM to generate new, original text, rather than reproducing or distributing the original works. The court analogized this process to human learning, emphasizing that copyright law does not extend to the methods, concepts, or principles embodied in a work."
Emphasis mine. Both the development of AI systems which modelled them after human learning, as well as the courts which in their ruling analogised it with human learning disagreed with you. And even if your want to argue against the logic, the legal system doesn't care, a precedent that AI training is learning and not copying has been set.