What, I asked McNeany, is the secret? Why should anyone expect a private firm to be better at running a comprehensive than people who have spent a lifetime working in the state sector? Come on, I said, cut the waffle: what would you actually do that would make a difference? Perhaps McNeany was protecting trade secrets, but I left disappointed. He talked a lot about "empowerment" and"targets" but, when I pressed him, he muttered, "these things are by their nature vague".
I shall have a stab at being more specific. The advantage of a private company is that it doesn't have to be accountable for what it does in the same way as a public body. It will have to meet its targets, to be sure, but the procedures it uses will not be open to scrutiny in the same way. In other words, it can cut corners, take risks, try out new ideas, use its imagination. This can produce speedier, more decisive and more flexible management than that in the public sector, where everybody's instinct is to follow the rules meticulously and, if in doubt, refer upwards.
The private sector, therefore, is not full of evil people, nor is the public sector full of time-serving dinosaurs. One is about profit, the other about accountability. There is space for both in the world. The trick is to decide how much space each should occupy. We should not, I think, be dogmatic in defending the traditional boundaries.
What matters about the state education system is that it is tax-based and universal. If Nrd Anglia takes over the design of the autumn-term timetable, orders the new desks, balances the budget, and explains to Mrs Bloggins why her daughter can't come to school with a ring in her nostril, who cares? You may argue that Mrs Bloggins loses the right to complain to her local councillor about the school's behaviour, but that may be a price worth paying.
I have to laugh when I hear Westminster politicians extolling enterprise and individual initiative and demanding more diversity in state schools. Who is responsible for driving these virtues out of the education system? Once, they existed in abundance. Think of Henry Morris and the village colleges of Cambridgeshire or of Sir Alec Clegg and the primary schools of the West Riding. We forget that most of what we now take for granted - comprehensives, equal opportunities, the GCSE, nurseries, even delegation of budgets - began as local initiatives. For 25 years, civil servants and ministers, acting in the name of accountability, have squeezed adventure and innovation out of the system.
Anything out of the ordinary has been denounced as sloppy, 1960s-style trendiness. One of the attractions of teaching used to be its professional independence; now, it has a national curriculum and national literacy and numeracy hours. Then Whitehall has the cheek to complain that everything is bog standard.
And that, I suspect, is the true story. He didn't articulate it very well but, when McNeany talked about empowerment, he had a point. Who now, if they wanted to be empowered in their working lives, would go into state-school teaching? Talent, dynamism, vision and initiative are being driven out of teaching, as they have been driven out of the rest of the public sector. The politicians have themselves created a desert. Now they have to call in the likes of Nord Anglia to make it flourish again.
Peter Wilby is editor of the "New Statesman"