Why would those correlations invalidate it, assuming we have controlled for origin and education, and are sampling society with low disparity? (e.g. western Europe).

Don't forget we have a direct causal mechanism at work; failure to predict; and we are not concerned with the feelings so much as with the regrettable actions themselves (and thus don't need to care if the intelligent people e.g. regret for longer, or intelligent people notice more often that they could have done better, which can easily result in more intelligent people experiencing feeling of regret more often). Not just that, but ability to predict is part of definition of intelligence.

edit: another direct causal mechanism: more intelligent people tend to have larger set of opportunities (even given same start in life), allowing them to take less risky courses of action, which can be predicted better (e.g. more intelligent people tend to be able to make more money, and consequently have a lower need to commit crime; when committing crime more intelligent people process a larger selection of paths for each goal, and can choose paths with lower risk of getting caught, including subtle unethical high pay off scenarios not classified as crime). The result is that intelligence allows to accommodate for values such as regret better. This is not something that invalidates the effect, but is rather part of effect.