This doesn't seem entirely true though - especially with news. There's a central organization at, say, Slate, that's responsible for hiring, editing, and fact-checking what they publish. Sure, some writers are going to be better/worse than others, but an organization that hires and retains bad writers who do bad research and editors who don't catch it, even when it's been pointed out, is an organization where you should have concerns elsewhere.
The proposition isn't that one bad article means everything will be false forever, but that you should approach all articles with some skepticism that the author/editor knows what they're talking about. Especially when you know from past evidence that they will publish things that you know to be wrong or misinformed.
It's not much different than how folks are getting concerned about counterfeit things on Amazon. I don't think that every product on Amazon is fake, and I don't think the fakes are evenly distributed across all categories. That doesn't mean I shouldn't check most things I buy to make sure they're safe when I know that Amazon doesn't seem to care if they ship me defective or counterfeit products.
You're making a straw-man of what the Effect is trying to get at. It's not saying one bad article means every single article is fully false, or that you shouldn't trust the sports scores, or Cathy is giving you bad life advice. It's just stating that we tend to not realize that one bad article may be a sign of more intrinsic bad editorial practices at a publisher.