Having read the comments but not the article I was going to wade in with some indignation based on knowledge of Her Holle's local school options, and Sevenoaks in particular.
He could have had a German education with diversity if his twins had taken the well trodden path through the German School and then IB at Richmond Sixth Form College where the German students underpinned excellent results and leaver destinations (no longer available due to the LAs ironically named "Choice and Diversity" Educational Strategy which provides choice only to those willing to sit in pews or move house, and diversity only in terms of families who know how to play the game) where they would have found all the diversity going amongst the 2000 students including some serious stoners and the odd stabbing
Private London Day Schools are not a commodity and there is a lot of variation in ethos and in particular bursary provision and it's effectiveness in widening diversity. Boarding Schools even more so. All the families and indeed, staff I know at Sevenoaks have picked it for it's down to earth ethos, IB, mix of day and boarders (it is not some Ivory Towers surrounded by high walls) and innovative MFL provision (that includes some families who are from ethnic minorities).
But now I am on a device the Telegraph has not put behind the paywall I have actually read the article and find myself having some empathy with him.
Do I regret sending my DCs to Private Schools. No, and he is not doing so either for similar reasons. He says he chose to do so because he wanted the best education and he wanted them to grow up with a dominant culture. A lot of third country kids are educated in one culture for that reason. Many expats, especially ones that grew up as third country kids, around the world bring up or educate their children in a dominant culture, even if that means families being parted or uprooted, because it helps to define their identity. Insight into other cultures is one thing, not knowing where you belong quite another.
Do I regret the limited diversity in my DC's schools? Ethnically, no. There was greater ethnic diversity than in local state schools, apart from the superselectives where nearly 70% are BME (which raises another set of issues). But socially, yes, inevitably they did not mix with a cross section of society. We made sure they did outside school but whilst there was a mix of the materialistic and those with more down to earth values at school they did feel frequently a bit exasperated with some of the narrow mindedness. You have to wonder when a geography trip includes a coach tour of the valleys highlighting manifestations of deprivation including "on the left a pregnant teenager" ....... So yes like Herr Holle I do regret that they did not experience the diversity there was at my state school (in my case a Northern Direct Grant Grammar)
Do I think they had a better education at a private school over outstanding state alternatives? Yes and No. I certainly think they had access to greater opportunities to pursue their interests in school, and more support in achieving their academic ambitions (particularly in the context of SpLDs). They probably achieved marginally better results but I don't think their ultimate destinations would have been different, or at least not if I had anything to do with it (by which I mean encouraging them in their interests and ambitions, not forcing them down any particular route). There was certainly some iffy teaching along the way from teachers who could rely on motivated pupils to achieve in spite of them. It was different, but better? Not so sure (though I am sure that my daughter was right to feel the ethos and atmosphere at the superselective was not right for her).
So in the end I think that he is providing a valid personal perspective.