It's never the case that someone misunderstood what scientist wrote. Much like the scientific papers, news articles, including those reporting specifically on the discovery, have their own goals, and the paper being cited is used as evidence or argument for article's own "study". Except for press, the standard is rhetorical, not scientific, it's the conclusions and not the methods that are "pre-registered" at the start, and claims are defended by "hey it's just a point of view", not by statistical significance.
In your own example of worst offender: the scientific study was trying to establish and quantify the connection between X and Y. The summary article was trying to push the angle that "this institution is doing important work". It started with that conclusion, and the paper cited was just the first thing the author found that could be easily massaged into supporting that conclusions by rhetorical standards.
Same paper might get cited by journalist trying to push for "X is bad for you", and they'll do roughly the same as the summary article. And, same paper may be cited by someone claiming they have a miracle cure for Y, and they'll make a honest observation that "absence of X reducing Y is a common bullshit claim based on misunderstanding the paper [citation], that actually shows there's no correlation there, I mean look at the confidence intervals, even the author says that in text nobody bothers to read"... - citation may be honest, but the article itself is still using it to prop up a different flavor of bullshit.
TL;DR: don't believe news. It's bad for your mental and physical health (p<00.05).