>The article can tell "Cort was informed about the new techniques from a family member back from Jamaica". How do you verify that? The only way is to redo the all work from scratch, refound all the historical references and cross-validate each of them. It's a huge work.
You start by going through the citations the author has listed and seeing if those support their reasoning. Sounds like that's what the non-expert in the linked article did. It turned out that some of what she claimed was not supported by or was in direct opposition to the sources in her citations. That's what citations are for. They're listed at the end of the paper in a standardized way so they can be easily accessed by anyone who wants to know where an author got a piece of information from.
If this wasn't possible, there would be no point to peer review. I can understand an article getting through where the author falsified experimental data. That's hard to refute unless you can find evidence of the false data or you run the experiment again yourself. A history article, though? If you're not double-checking dubious claims by see what sources the author is using to support them, you may as well not bother reviewing.