Having just read the article referred to in the OP, the writer's main arguments for preferring to send his kids to an independent school are based on snobbery and personal anecdotes about the state schools he has worked in.
He talks about the "mad dash" of staff out the door at 4pm; clearly this varies from one individual to the next, and as a part timer I don't stay on site after hours as I collect my own kids. However, the majority of my full time colleagues run a raft of after school activities, from DofE to drama, revision classes and sports activities. And even though I leave when I've completed my teaching hours, I put in 45-60mns of preparation & marking for each hour I teach + the time to complete administrative jobs - once my own kids are in bed.
Then the writer says he'd like for his kids not to mix with kids who "punctuate their speech with innit" - reflecting his own class hang ups and lack of tolerance.
He then goes on to assert about the thousands of kids who's future are "blighted" because they're not getting the exam results they should, because of the "thousands" of useless state school teachers. Unsubstantiated teacher bashing. There is a plethora of reasons why some children don't achieve the results they want and need - but to heap the blame on "work-shy" teachers is naive.
Whilst I agree that the staff:student ratios in independent schools are much better - and the main reason why I'd consider sending the DCs to an independent school (if I had the huge income required), to imply that teachers in state schools are not focussed on the needs of the children they teach is just bashing for the sake of it. In all the state schools I've worked in, we have had weekly whole school briefings where pastoral issues have been flagged up, faculty meetings where similar information is shared, and with email, I receive daily information or calls for info for specific individuals. We also have a centralised database which allows for information about students to be shared between staff and the students' parents in real time. As a school, we work together to ensure that children's needs are met, to the very best of our abilities.
On a personal level, I have a first degree, a master's degree, a PGCE, and nearly 10+ years' teaching experience. There is only one teacher in our school (of 50+ PT and FT teaching staff) who is 'unqualified', and she is currently working towards QTS. There is a good mix of newly qualified and experienced teachers in my current school, where ongoing training and performance review is taken very seriously. Our school was classed as 'good' according to OfSTED, is truly non selective, and is in an area which is semi rural. To be honest, not all schools will be able to provide such a good education for the children in their care, but to suggest that that comes down to a culture of laziness amongst the staff is really disingenuous: social and economic factors, funding levels, whether or not the school is in a grammar school area (which means that other schools in the area cannot be non-selective, as the more able students will attend those grammars), are all hugely important factors.
Towards the end of the article, the writer says that the few people he polled as to why they had chosen independent schools both mentioned the "ties" and friendships that their children would form. I think this is often a prime motivator in sending children to paying schools - you pay for your child to enter a network where, on average, children will enter more lucrative professions or simply have wealthier backgrounds. It doesn't mean that state schools are not offering some good teaching and great extra curricular activities to their students though.