Ime there's not a one size fits all rule, it varies with species. Some of it might relate to conditions in their native habitat, but not always. A species or population might live in a very specific location with specific conditions while close relatives are adapted to a range of habitats and conditions, so they may generally be a fairly adaptable fish, but even this is a case by case thing. Discus for example-- According to Bleher, two types (green and Heckel) live in pretty narrow water conditions, while (what he calls Haraldi) live in a wider range of temperature/ph than most people suspect of discus. By now, many, maybe most, cultivated strains are comfortable in conditions they'd never see in the wild.
In any case, it's a question of range of comfort zone and some species are simply more adaptable than others ime. It's not just about HITH or infections. Some types hardy enough to be healthy with good nutrition and clean water may still live shorter lives at the fringes of their range of tolerance. Some get more tense, more skittish when water's out of their comfort zone. Some do just fine, themselves, in a range of conditions that their eggs or fry can't handle.
Ime you can't generalize, it pays to do some research with unfamiliar fish. Some fish are more adaptable than people think. Then again, you might come to conclusions based on experience with others of a type that don't always work. I've found Heros species to generally be forgiving and adaptable, including wild, but was talking (email) with Jeff Rapps a month or so ago about Inirida and he says he's found them to be an "obligate" black water fish.