Nope! I just did some additional experimentation and found that my original guess was incorrect as is your URL guess.
It hinges on your nytimes.com cookie or lack thereof.
If I visit the website without a cookie in place I can navigate from article to article; once I get a cookie, either by visiting nytimes.com directly or clicking on a link, however, I'm at a dead end in all respects.
...more or less, anyhow...
