Difficult to do if you aren't even tracking what applications are legacy in the first place, they'd at least have to ask a sample of admitted and rejected students post facto.

Ah. I assumed in this scenario we had some mechanism to determine who is a legacy applicant (or not). You make a good point.

If ability has a strong genetic component, one would expect a higher acceptance of legacy students.

Even if ability has a strong nurture component, one would expect the same.