Some things do have simple neat correct explanations though. So it reduces to a tautology - "be suspicious of simple explanations in areas where you wouldn't expect a simple explanation to work".
I’d argue that as a non-expert you can’t really assess whether a simple explanation would work or not, and therefore you’d have to be suspicious about having expectations that it would.
If you lack expertise enough to say if a simple explanation works, you lack expertise in complex ones too, and should probably stop trying to guess what's right based on very weak signals. Which was my original point.
I think this is what the article alludes to. There is the famous example of some expert on Rembrandt (or some other painter) that could tell that a specific painting was a forgery, but was not able to pinpoint why he felt that way. (This anecdote might have been in the introduction of some book on intuition, something Malcolm Gladwell-ish, but I can't recall which...)
I read this a bit differently: Experts often have a hard time explaining their intuitions. That is, they (presumably, as experts) have the correct intuition, but can’t articulate their internal reasoning (and maybe the correct explanation is inherently difficult to understand), while on the other hand it is not very hard to come up with a seemingly coherent ("neat") explanation for pretty much anything. If that is indeed true (I don’t know that it is), then having a "neat" explanation presented could really be a counter-indication, statistically speaking.
I’m halfway sympathetic to that, as "neat" explanations do quite often oversimplify, and reality usually turns out to be more complex. Explanations that also point out their own limitations and caveats tend to inspire higher credence.