That's a bit of a stretch. The NY Post is a tabloid [1]. Tabloids are technically newspapers, but they aim primarily to sensationalize [2].
Tabloids are nothing like the NY Times or Washington Post, which attempt to present objective, unbiased news. (Now you may argue that they fail at that -- but they do profess at least to aim for it, while tabloids don't even try in the first place.)
So seeing a tabloid article flagged doesn't seem all that different from a blog post being flagged. Seeing the NYT or WaPo flagged, on the other hand, would be highly unusual.
(I'm neither defending not criticizing FB/Twitter here, but just pointing out that the NY Post shouldn't be held up as even remotely a trustworthy source of reporting.)