The effect is definitely real - it happened to me many times, when I trust journalists in topics in which I have no expertise, sometimes much more than I should have, to my eventual regret. All while knowing to be extremely careful trusting anything in the press - especially non-specialized press - in my area of expertise, since the coverage is so universally bad that it's a cause for celebration when at least something correct and non-distorted comes through. I know that, and then kinda forget that, because questioning literally everything is kinda exhausting.
I am not sure what you mean by counter-example to the effect - I do not think the idea is that it's always happens. It's just the name and description of the thing that sometimes happens.
I'm sure the effect is exaggerated because it gives people the warm fuzzies to know they're smarter than those newspaper dolts, but demonstrating a few news articles were correct doesn't seem like it proves all reporting is correct.
Although perhaps there is actually the opposite effect. Now people read an article in their field, notice some flaws, and conclude all reporting is terribly flawed?
But really, one month you read a wired article about kaminsky and the keys to the internet, and then you read an article about hacking slot machines, and you think, oh yeah, I'm sure this accurate?
It's really easy to cite counterexamples to it. Even in our field, and in very mainstream press outlets.