It would be slight if the admission rate for comparable non-legacy applicants was 25-30%, not 6%. The 6% average overall admission rate likely includes all sorts of people whose admission likelihood is essentially 0%. While the legacy pool may also contain some no-chance applicants, by and large one would expect the legacy applicant base to have more than average understanding of Harvard admission standards, and not to submit hopeless applications. I know that has generally been the case with my Yale alumni/legacy cohort and Yale applications: the acceptance rate runs around 25%, but kids don’t apply unless they have a pretty good argument for admission.
For years, there was folklore from various sources that after every year’s acceptances went out the Harvard admissions department would compare its acceptance rate for Harvard legacies to its acceptance rate for Princeton and Yale legacies (who of course received no special consideration at Harvard unless they were also Harvard legacies, in which case they were in the first group, not the second). The point was to create an artificial control group consisting of a population that would be demographically very similar to the Harvard legacies in ways that were significant (including things like family attitude towards higher education and the liberal arts), and to see how much of a boost the Harvard legacies actually got. The answer, supposedly, was “no meaningful advantage,” i.e., the rate at which Harvard accepted Harvard legacies was only slightly higher than the rate at which it accepted Yale legacies.
Indeed, many of the Yale or Harvard legacies I know who were accepted at their legacy college were also accepted everywhere else or almost everywhere else they applied, if they applied elsewhere. The last of my many cousins to go to Harvard went as a third-generation legacy, but she turned down actual RD acceptances from Stanford, Yale, Princeton, MIT, and Columbia in order to attend Harvard.