I'd imagine a group's ideas are more to do with non-genetic factors than genetic intelligence.

As would I. But the claimant's intelligence (whether genetic or otherwise) is nevertheless a factor I take into account when deciding how much weight to give a claim.

And, yes, all of this is contingent on the idea that IQ correlates well with intelligence.

And, yes, if it turns out that the physiological mechanisms whereby group A develops greater intelligence than group B are heavily environmentally mediated (e.g., due to differential poverty, nourishment, or other factors) I might well decide to alter the environment to increase intelligence in group B as well.