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Actually I have a somewhat different interpretation.   This is partly based on my experience in the US.   

The high school my daughter attends is a public high school (i.e. supported by local tax dollars - I know that the terms "public" and "private" get reversed in the UK, so I'm trying to be careful here).   By and large, I would say that many, if not most, of the students I see at Harvard are less qualified  - or let's say, less "broadly educated" than the upper 30-40% of students graduating from this high school.   

So, what's going on in admissions?   I think it's not just a question of rich kids buying their way in - I think it has to do with what many people call "pointy" individuals, which may also relate to money, but in a less direct fashion.   This means that they do an amazing job at just one thing.   In many cases this 'one thing' can be a bit of a sham.   Let's say they have on their college resume a statement that they did fund raising in the US and then founded an orphanage in Guatemala.   This scores huge points with the admissions committees who want some characteristics beyond good grades. It may turn out that the orphanage in Guatemala wasn't really an orphanage - that kind of thing.  There are also students from disadvantaged areas who also come off as 'pointy' and lend to diversity of the school, and may even have the grades on paper, but it doesn't reflect what they really know.  

I sat on a committee to review students who were nominated for a prize for the 'best' (in some ill defined sense) freshman.   I read their essays, many of which were quite flawed, in my opinion, and also seemed to be all politically skewed and in the same direction.   Now, my politics may be fairly liberal, but I don't particularly like to award 'points' for gaming the system by appealing to what might be the typical mindset of a professor here.   I want substance.  

As Frank pointed out, many of the students may be outstanding in one area, like history, but rather weak in other areas.

I do try to give the weaker students a chance to catch up, and I commissioned a video review of trigonometry.  Given that I've been dealt a hand by the admissions committee, I try to play it as best I can by giving reviews that don't drag down the rest of the class.   I hope that, and try to get, by the end, students who have some degree of skill in empirical reasoning, but it takes time, and often I have to overcome the desire on the part of the students to 'game the system', which happens too frequently.   This means that I have to try to 'out game' their attempts, which can be rather taxing.

Sorry for the length of this, but I've been struggling with this issue and in a way, writing helps me think through the issues.

Best,

John H.