That may be trueUnrelated to the Times, Post, or Atlantic...
One thing that @ThatOneDude using that site kind of illuminated to me is that most of the left-center sites score higher on the "factual" part of things than do the ones on the right-center. There are a few good sites on the right that are really fact based but most of the time they're a little lower on whatever the fact scale is.
And the further from the center they get the more ridiculous in regards to how much bullshit they throw out. That applies to either side.
But it loses some water when the “fact” checkers are usually left leaning and in case of some social media former democratic employees.