I'm not really sure how that follows. Was there some established link between GRE scores and ethics?

I suspect it has as much to do with the following requirements:

1) A degree that is take-home essay heavy. 2) Very vocational -- the goal being the degree, not the learning.

I'd expect business and law schools to be high on the list too, although maybe the dynamic is somewhat different for professional schools.

Suggested link is lack of brains, not lack of scruples - remember the shadow scholar's list of reasons includes 1 group that is simply too stupid to handle the work.

This would imply a large variance of ability in the group, not a lower average GRE score. Although it could be speculated that as the GRE score regresses to the mean (of the general population), the variance likely increases.