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.
I have seen low fidelity copies of motion pictures recorded by a handheld camera in a theater that I'm pretty sure most would qualify as infringing. The copied product is no doubt inferior, but still competes on price and convenience.
If someone does not wish to pay to read the New York Times then perhaps accepting the risk of non-perfect copies made by a LLM is an acceptable trade off for them to save a dime.