The math doesn't really work out on this. Only 0.5% of people make a 40+, and of those only a small fraction will have 4.0 GPAs to go with it. Even if we say the 3.8+ bin is half 4.0s you're looking at a pool of ~150 people. The med schools currently holding top 1-2% medians have a combined class size of over 1000 each year. They really couldn't get medians that high. A place like WashU at a 3.9/38 is already going very hard for stats.
I think you're using conservative stats. From what I could find, 86,000 people took the MCAT in 2011, which means 40+, again using your stat of 0.5%, would mean ~400 in that range. Do you know the yield for a place like Harvard? Like 75-80%? I'll ask you an honest question. Do you really think a 4.0/40 with minimal shadowing/volunteer/etc. is going to get into Harvard or WashU?
If your answer is yes, then we have nothing to discuss further. I simply believe they would not.
If your answer is no, then it must necessarily follow that stats don't get you into the top med schools. Other factors do. You already answered this with your statement that there is more to admissions than just stats. Where we differ is that you seem to think stats play a dominating role in admissions whereas I believe that it does not - it only serves as a measure of the level at which you are performing. For simplicity, we can say top schools want students who excel and mid- and low-tier schools want students who can handle medical coursework. The bar for the former is higher than the bar for the latter (say 35+ vs. 30+). These are two completely different admissions stories we're talking about so let's keep it clear for everyone else.
Well, from speaking with people with experience in admissions at WashU, I can tell you it's not the same reality for all applicants. According to one advisor 90% of personal statements are meh, 5% being terrible and 5% telling a very interesting life story that helps. You go into interview day with different interest ranks here and are adjusted up and down from interview day, not viewed as total equals coming in. A school claiming they use stats only to judge competency and then maintaining a median of 37-38 every year should seem odd.
I'm not saying top schools use stats only to judge whether students can handle medical coursework. I think in a response to you before, I noted that top schools likely use stats to judge whether students can
excel in their program and whether they can become future leaders in the field. In that case, you need more than a 30. You need 35+ to show that you can excel in their program. Of those who have those scores, other factors decide whether you are admitted.
Now, I do think there is more to admissions than just stats. But, the naive position is thinking everyone with the stats to handle med school (which is like a 3.6 / 30) is on equal footing for top programs as long as they are interesting and interview well. A 40 alone won't get you into WashU, but swapping a 30 for a 40 on an applicant can certainly change whether they are interviewed, and not because it predicts struggling to handle med school.
You can continue arguing against a straw man if you would like. But again, if you read my response to your post above, I clearly noted that a 30 and a 40 are not the same for top schools because top schools use stats to assess whether you have the potential to become a leader in the field and whether you can
excel. That's not the same as saying you have competency - this goes beyond that. I may not have been clear about this in some posts for the sake of brevity, but I am making it explicit now.
I will also say that my belief is grounded in stats from my own former undergraduate college which was one of the elite schools in which Harvard, WashU, and Yale were among the medical schools that extended the most offers to students. The average GPA of admitted students from my college to those med schools is lower than that of the average matriculant to those schools. If those schools wanted to fill their class with high stats, they could. But we do very well at those schools despite our lower stats which, to me, means that we are viewed in the same light as applicants with higher stats. In other words, our stats showed that we are able to handle the rigor of medical coursework at the level of those schools because our stats were within the right range (as I initially said, there is little difference between a 3.7 and 4.0 student) and other factors resulted in admission.
This whole discussion has gone on a lot longer than I intended it to. I'm here only to speak my own beliefs. You can believe them or not, but I stick by them based on my experience with grading courses, teaching, and interacting with support staff from my former undergraduate institution.