Dunning Kruger does not mean that unskilled people think they do better than skilled people. On average, the more competent people at any skill will rate their abilities higher than the less competent people. See this graph[0] from the original study[1] for a better explanation.
I meant it the other way round: That some smart people won't have that "I show 'em" attitude and won't even try because they think they are too bad anyways.
[0]: https://fbcdn-sphotos-b-a.akamaihd.net/hphotos-ak-ash4/p480x...
[1]: http://ttsg.org/pdfs/Dunning-Kruger%20Effect.pdf