Traditionally, "intelligence" (as colloquially defined) has correlated with type 2 thinking. So, a reasonable conjecture would be that people who are better at type 2 thinking would use it more and, therefore be less vulnerable to bias. However, this research shows that even those who are very good at type 2 thinking (as measured by their SAT scores and NCS scores) are even more vulnerable to cognitive biases. This is a deeply counter-intuitive result. Why is it that people who have a greater capacity to overcome bias have a greater vulnerability to bias?
Overconfidence. If you've become accustomed to thinking of yourself as being better able to avoid cognitive bias, you come to be confident in your abilities, to the point where you (perhaps unconsciously) think of yourself as not susceptible to biases.
Why do you assume that type 2 people have greater capacity to overcome bias?