For a counterpoint on why this story is likely BS: https://talkingpointsmemo.com/fivepoints/5-points-on-why-the...
It likely is BS, but not definitely. Even some of the points in the TPM article aren't very strong (I'm sorry, but journalists mocking the story isn't a point.) But, even if it is, it's not the role of Facebook to decide it is or isn't, when it is not verify-ably false. Instead they should just elevate critics of the article/scoop like the article you linked.
The people who wrote the NY Post piece had plenty of time to prepare. Now the story is rocketing around at the speed of the internet; but it takes time to refute authoritatively.
Twitter, Facebook, HN, and similar channels will have spread the story regardless of its truth or untruth. They are vulnerable to propaganda, similar to how open relays are to spreading spam.