Prompt injecting their own article would indeed be an incredible show of incompetence by the New York Times. I'm confident that they're not so dumb that they put their article in their prompt and were astonished when the reply could reproduce the prompt.
Rather, the actual culprit is almost certainly overfitting. The articles in question were pasted many times on different websites, showing up in the training data repeatedly. Enough of this leads to memorization.
