From what I can tell, this has nothing to do with LLMs at all. In the example in the article, the user is asking Bing to go fetch the contents of an article directly from the website, and print it out, which it dutifully does.
Seems like the "problem" is that NYT etc gives privileged access to search engines for indexing their content, but then get upset when snippets of the indexed content is being shown to users without the users having to fight the paywall or whatever.
This article also claims that the screenshot is coming from ChatGPT when it clearly is not.