If you read carefully, I clearly state that the GRE is probably the reason most people make it past the first cut, hence the "one foot in the door" remark. I'm willing to believe that most programs have a bottom-line GRE score they use to filter applications, and most applications probably never meet a pair of eyeballs. If you happen to survive the first cut, your GRE scores probably matter less than your other application materials (SoP, writing sample, LoR), at least I would imagine (I guarantee you I have lower GRE scores than a lot of people who were rejected to Cornell). So, to recap: GRE scores are probably important during the first application screening, and therefore party responsible for any offer you may potentially receive, but less important in the later stages of the admissions process.