Say, for example, that there's an article about a "scientific study", claiming some strong conclusion (e.g. "pig hair cures diabetes.") The article goes on to say that the study has one data-point and no control-group (which is to say, basically, that it's an anecdote.)

To still even consider the study's conclusion as possibly true is to privilege the hypothesis. You didn't have any facts before. You don't have any facts after. And yet, your default has switched from "assume pig hair has no special properties whatsoever" to "assume pig hair maybe has something with a vaguely-medicinal use in it." You've updated on zero information.

Just as much as publicizing such a "study", it's irresponsible to put such journalism--sophistry, really--in front of other people, where it could possibly infect their defaults. Not everyone catches these things. Most people only read the first paragraph or two of things, and come away with impressions. These impressions, especially in the case of really bad journalism, can be directly opposed to the impressions they should have taken.

If we are a community here, then we should want to help one-another avoid bad journalism, and more importantly, avoid becoming swayed by whatever the bad journalism purports to report. We don't all need to think the same thing--but supporting a story just on the basis that other people support it, leads to pig hair being "signal-boosted" into notoriety.