I agree, and one place I've observed this is in quantum physics. The double slit experiment is an experiment where you shine light through two slits, and instead of the expected two bands, it makes a wave-like interference pattern. This single experiment changed how we view all of physics. However, nearly every source targeted at laypeople claims that there is a variation where you can put a detector on one of the slits and it will show two bands. This is false.
One clue is that these claims never detail on what this "detector" is. There are various types of detectors, and instead of showing a two band pattern they show a single slit interference pattern. By not giving specifics, the claim becomes much harder to disprove. This may not be malicious though, as the source of the faulty claim is likely the miscommunication of a thought experiment proposed by Einstein. Einstein proved by thought experiment that any detector couldn't show an interference pattern, which is easily twisted into the incorrect claim that it does show the two band pattern that people initially expected.
Even with all that, it's simply hard to refute. Like you said, it requires rigorous technical arguments, specifically as the faulty claim didn't specify what kind of detector they use. So the layperson has to choose between <some detector makes shape you'd expect> and <multiple complex existing detectors makes different shape>.
In the end, to a layperson, it wouldn't even seem to be all that important. And yet, almost all of the misunderstandings people have about quantum physics come from this one faulty claim. This claim makes it seem like some objects have quantum behavior, and some don't, and that you can change an object from quantum to non-quantum by detecting it. When in reality, all objects have quantum behavior, we just don't usually notice it.