Indy or are helped out by a bursary? or their parents are staff? I cannot comment on the detailed financial arrangements of my DDs' peers parents, just that not only are there next to no uber rich global elite at these schools but the offspring of wealthy city lawyers, bankers etc are also far from in the majority, there alongside the children of professionals, some from poorer backgrounds presumably benefiting from bursaries and a fairly healthy representation of immigrant communities from Eastern Europe, the Indian subcontinent and Asia. You clearly do not need to be earning £250k
What they do have in common though is that they are very clever and I think that is where this story originates. Without a doubt you have to be cleverer to get into these schools than ever before, because there are more pupils chasing places, a combination of the aspirations that were encouraged in the children of Thatcher's Britain, and are strong in immigrant communities, and the shortage of good state school places. I also think the schools have got better at identifying potential, certainly what split the less selective school exams from the most selective was that they really aimed to test ability with some very stiff testing of reasoning and lateral thinking, you can't buy a place in these schools with tutoring etc.
When my older daughter sat these tests overseas from the equivalent of a state primary, I naively helped her cover the bits of the curriculum she hadn't studied and thought that if she was bright enough she would get in and if not there were plenty of other less selective good private schools around here that would enable her to achieve her potential (at a rough count ten easily accessible from here that enable their brightest pupils to get strings of A*s and to the best universities). Except I wasn't naïve and she did get in, even to the most selective. Four years later when my DD2 sat the exams I developed the skills of a SAS hostage rescuer so quickly did I get her out of her non selective prep playground and the miasma of competitive and anxious parenting, Chinese whispers of what you have to do to get in, secret tutoring that bordered on abuse and putting pressure on the school to do whatever they considered, on the flimsiest of evidence, was needed to get their DDs into the best schools (determined according to a subjective league table that makes yawning gaps of the tiniest difference in results etc. ) Then when the pupils (along with their state school peers) got into the schools that were right for them, but not necessarily in line with parental aspirations, there was all manner of handwringing and justification , all designed to deny that the reason their DDs did not get in was simply because they were not clever enough. They will love this article.
I do seem to remember the implication that Abromovitch bought a place for his DD by purchasing the church opposite and making it into an arts centre 
It is this level of competitive parenting that has made it more and more difficult to get into these schools and of course clever pupils equal stellar results, but then clever pupils get good results whether they go to elite private schools, less elite private schools, grammar schools or are in the top sets at outstanding comps.