I think it’s more nuanced than that.
Extending the “monkeys on typewriters” example, it would be like training and evolving those monkeys using Shakespeare as the training target.
Eventually they will evolve to write content more Shakespeare like. If they get so close to the target that some of them start reciting the Shakespeare they were trained on, you can’t really claim it was random.
If the argument is that people can use ChatGPT to get old NYT content for free, that can be illustrated simply enough, but as another commenter pointed out, it doesn't really seem to be that simple.