I think most of the time it's really not going to be as hard as all that, because the problem is something like, article makes broad claim based on a very easy to understand study where the data is results of survey questions. The paper clearly and explicitly outlined caveats and qualifications for their results, but the article chose to ignore these, so all that would be required to call them out on it is basic reading comprehension and the ability to copy paste a brief quote from the paper. Or maybe there are stark, obvious differences between the question asked in a survey and the claim of a clickbait headline.

Even for something more complex, if the paper is well written I think people without a background in the field could get stuff out of it, at least enough to spot direct contradictions between it and a summary. It's just reading. A lot of people can read and have some higher education.

For that wikipedia article, I think it would make more sense if it expanded on "may differ slightly" and how that interacts with this criticism of black hole information transfer being impossible. Would that criticism imply the parameters for new universes must be always the same? Have infinite variance with no reference point? Not exist at all? Is "may differ slightly" a claim that each universe is a reference point around which the cosmological constants of child universes randomly vary a little bit and then there could be drift based on which constants result in a universe with more black holes? If that stuff was concisely clarified it would probably seem less arcane.