There’s a chance that universities, like most things, have changed a bit since I was bluffing my way around Edinburgh’s George Square. It’s not clear that students work harder now, but there seems to be a dismal fad for making them prove it, poor souls. Whatever next?

That apart, I suspect that what some call “the university experience” is much as it ever was. From all I hear, a student from a state school can still be regarded as having done awfully well, really, just for gaining entrance to certain institutions. “Access,” they say, is the issue, together with “attainment”. There is nothing remotely new about that. The fact alone is worth bearing in mind.

Clearly, nevertheless, we should worry if, as we reported yesterday, just 1,335 school-leavers from the poorest 20 per cent of households went to a Scottish university in 2013/14 compared to 5,520 from the richest 20 per cent. Clearly, too, we should be doing something to address a glaring disparity if minimal lip service is to be paid to that vague, convenient notion “equality of opportunity”.

There is no shortage of suggestions. Conservative opinion would have it, as ever, that the failures of state school pupils, perceived or actual, have to be a result of state education. That stands to what they know as reason. Where Scotland is concerned the ambition, predictably, is to import English reforms, whether so-called free schools or tuition fees, weaken the control of local authorities and the state, and bring back selection for good measure.

The prospectus is familiar. The habit of conscripting the poorest as human shields for some right-wing manoeuvring is an old, tried-and tested technique. But if the statistics tell a story – and they do – who can blame Tory ideologues for writing their favourite conclusions? What’s the alternative?

The Scottish Government’s Commission on Widening Access says universities should consider accepting poorer candidates with significantly lower grades than their middle-class counterparts. It countenances the latter losing out, but defends the idea on the grounds of equity. It also cites evidence to show that lower grades are no guide to future attainment if the right support is offered.

If the aim was to introduce the pigeons to the cat, that ought to do it. You hardly need to guess at the likely reaction. First will come the all-purpose charge of dumbing down. Then there will be the claim that bright, hard-working middle-class pupils are being punished for the failings of state education. Then there will be the accusation that the commission is trying to rig the game rather than improve the quality of the weakest players.

How weak are they, though? Or rather, why is it self-evident that state education is an inferior product? There is certainly evidence enough to say that class matters where access is concerned. Evidence that state schools are therefore at fault is specious logic. Other things are going on if, as the commission maintains, “bright students from deprived backgrounds can enhance, rather than jeopardise, academic excellence” when they are properly supported, even with inferior grades.

Poverty, in any case, does not explain everything. This week, the Institute for Fiscal Studies produced work to show that poor “white British” pupils are on average least likely to go to university. The study also found that the proportion of candidates from ethnic minorities attempting higher education is “very high on average”. Youngsters from Chinese and Indian backgrounds, in particular, are most likely to enter university.

You might have presumed as much. Would you also have guessed that the poorest pupils of Chinese origin are more likely to go to university than the richest white pupils? That almost as high a proportion of poor Indian youngsters apply to universities as the wealthiest white British youths? If poverty is no hindrance for ethnic minorities neither, patently, is state education.

Still, what might they not achieve if their schools were liberated from government, or were, better still, the finest private establishments? This is another of those facts of British life by which effects are taken to demonstrate causes. People (often the beneficiaries) look at the social mix of students in the Russell Group universities, led by Oxbridge, and infer the superiority of private schools. The possibility that dominance and superiority are not one and the same is not considered.

On that front, there was more inconvenient evidence this week. For obvious reasons, the representatives of private education were not impressed, but research carried out by Cambridge Assessment, a department of Cambridge University, was unequivocal. As far as England is concerned, state school pupils are likely to do better at university, in terms of degrees achieved, than private school counterparts with similar A-level results.

The finding was not entirely new. A dozen years back, a large-scale project conducted by the Higher Education Funding Council for England (HEFC) found that state school pupils were achieving better degree results than comparative students educated in the private sector. In other words, if they began with similar qualifications, the state school pupils performed to a higher level.

Questions arise from such findings, even in crude summary. Clearly, what state school pupils lack is the opportunity to compete, rather than the ability. The success of ethnic minorities makes one point, the contest for attainment in degrees another. State education is not, of itself, in any sense inferior. Attempting to take schools from local authority control is in essence irrelevant.

Why, though, are there such disparities? You could as well ask why private education looks like an expensive failure, at least in the terms measured by Cambridge Assessment. Reasons for that have been sought since the HEFC did its work at the start of the century. Do students from private schools “socialise” overmuch? Do they socialise because they have no anxiety over their futures?

And is it an accident, precisely parallel, that less than five per cent of the intake at St Andrews and elsewhere comes from the poorest backgrounds? How about the fact that the private education sector, failing in straight university competition with state education, still manages to dominate British public life while accounting for less than 8 per cent of school pupils? Not quite the brightest and not quite the best, but still claiming the prizes?

My fitness to judge might be questionable. My only direct experience of schooling was with one of those comprehensives that are supposed to have caused such terrible damage to education in Britain. At Edinburgh, strange as it certainly seemed, it made me one of a minority, but somehow I managed to do better than some expensively-educated peers. Perhaps I was an anomaly.

If so, all those youngsters of Indian, Chinese, Bangladeshi and African origin must be anomalies too. Instead, I think they tell us that there are complicated rules to the attainment game, that expectations and assumptions count for as much as family circumstances, and that beating the system can be quite an inducement.

Rather than wreck state education, a country that sets such store by private schooling might pause to ask itself about the Cambridge Assessment findings. What’s the point of the best education money can buy if state pupils, given half a chance, perform better?