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In the original DK experiment they asked students after they had taken a test that where would their score end up compared to their classmates (which they had no knowledge of). Obviously they picked scores around the middle*

Which resulted in top students 'undervaluating themselves' and bottom students 'overestimating themselves'. Or under/overvaluating a random future variable that they don't have knowledge of, at least.

The original DK paper actually shows a positive correlation between the guesses and the test results: students are generally aware how they are among their peers, and smarter students guessed higher than studetns with less time to study on their hand.

This being said, the 'DK effect' is something people talk about, and it might exist, and it might be perceived by people. It's just that the original DK paper does not support it.

* another lesser talked problem with the DK paper is that people don't actually believe the answers they give, because the question is nonsensical.

If someone just takes a test, they won't think that "I'm sure I'll end up the 24% this time". Even if they are forced to anwser this question, even then they won't believe it, because that's not how random and future work. People are generally aware of about where they will perform (with positive correlation, in fact the original DK paper shows it) but they are not aware of results of specific, random future events, and they are not claiming that they know the results of specific, random future events, or believe it in their hearts.

DK paper tries to frame them as they were actually believing this, but they are not.

More to read at: https://en.wikipedia.org/wiki/Dunning-Kruger_effect

Can't we just get to the pop culture version of the DK effect by deduction?

It seems reasonable to assume that for some group of intellects they are not smart enough to know how not smart they are. There is no definite boundary where this effect is either on or off, therefore there are probably some gradations to this awareness as you climb up the intelligence ladder.

Another way of putting it: if dumb people had more insight they would cease to be dumb.