>But how did the candidates we selected measure up? The truth is, we got very mixed results. Many of them were average, very few were excellent, and some were absolutely awful fits for their positions. So at best, the interview had no actual effect on the quality of people we were selecting, and I'm afraid that at worst, we may have skewed the scale in favor of the bad ones.

This doesn't follow at all! Consider, as is surely the case, that only a small fraction of the applicants would have turned out to be average to excellent. The interview process can filter out the vast majority of the sub-average applicants and still leave you with a significant fraction of sub-average employees.