Never heard of this bloke so not really that bothered by what he has to say - what his motives are I'm not certain either.
He seems to fundamentally not understand some very basic "facts" concerning education which I should find odd, given that he is a HT.
However, you don't necessarily need to know much about the education system to be head of a private school. A friend of mine is a HT of a private school and has never worked in this country in the education system. I know he is very talented and I'm sure he does a very good job; I suspect his role is much more business / people management though.
My views -
"Better" schools in middle-class areas appear to do better than schools in less affluent areas often because of the catchment - children of accountants, doctors etc have people at home supporting and pushing them and academic success is an expectation. That is, of course, a generalisation but there is a lot of truth in it.
One expects the "better" schools to have "better" teachers. Where is the evidence for this? How would anyone be able to say with certainty where the "best" teachers are? How can they be judged? By exam results? Well that presumes that children achieve in line with the "ability" of their teacher. Well that's bollocks. So it isn't actually possible to say.
Thus, until anyone can pinpoint with 100% certainty what makes a school "better" than any other, any suggestion that parents should pay for one school over another is absurd and totally unworkable.
A friend of mine over coffee recently suggested children should all be given education "vouchers", to be cashed in and used whenever that child was ready to use them effectively. There are, in some schools, so many young people who aren't "ready" to learn when we want them to, and they largely are failed by our system as a result. They also disrupt the learning of those who are ready and want to do well. Brilliant idea. But just as cloud-cuckoo land.