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Well, this is true, but it's also hyperbole. It's not really everybody misunderstanding the problem so much as simply not caring. People are sloppy with the terms "NP-hard" and "NP-complete" and use them interchangeably because it's usually not important. Usually they mean "NP-hard", and that is the significant thing.

Yes, it's wrong to use "NP-complete", but plenty of people who thoroughly understand the problem do so. Welcome to Computer Science, sloppy is par for the course.



And usually they just need to say that it's intractable, unless they're speaking about some kind of solver or approximation classes.




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