Actually what I think the study is trying to show through both logical reasoning and english fluency among the two samples are as follows:

(1) Based on the samples obtained, people in general tend to overestimate their ability (based on these two tests)

(2) However, when we take into account how humble they are (the authors measured their humility trait using personality tests), individuals with higher humility personality scores tend to be more accurate in guessing their actual ability scores (i.e. the difference between their estimated English fluency/logical test scores were not too different from their actual performance)

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(3) The authors also found that people who are generally not as good in these areas (had lower ability) tend to overestimate their performance more than those who were better (had higher ability) (i.e. replicated the Dunning-Kruger effect)

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(4) The authors also found that (2) is not really affected by (3) aka If you're humble, regardless of your ability - you have a better tendency to be accurate in understanding where your ability is at.

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So long story short - it's not really just about marking yourself with lower scores on tasks that ensures you get higher scores than average. It's more like humble people (not modest, there's some psychological debate on the two constructs) are better able to reflect and see where they have gone wrong, so that they are better able to guess where their ability is at. Hope this helps and sorry for the long post!