The Scottish Government appears to have achieved the impossible: getting the national security whistle-blower, Edward Snowden, and the Institute of Directors to agree on something. The subject? That the Government's Higher Education Bill stinks.

Both seem to believe that the Education Secretary, Angela Constance, wants to abolish elected rectors in Scotland's ancient universities to impose central controls and undermine academic freedom. The Government insist the bill will do neither.

Elected rectors chair the governing bodies, the courts, of the ancient universities such as Edinburgh and Glasgow and have done since the 19th Century.

Now, I don't answer for the Government here but I have an interest. When I was rector of Edinburgh University I sat on the independent review on higher education governance under Ferdinand von Prondzynski, principal of Robert Gordons University. The Bill is supposed to be based on his recommendations.

To be absolutely clear: the intention was never to abolish elected rectors; far from it. The review recommended extending the principle to the many universities whose governing bodies do not have elected chairs.

So, Mr Snowden's claim that rectors are “being replaced by elected chairs of court” is nonsense. Rectors are elected chairmen and women of court even if Mr Snowden is unable to discharge this responsibility at Glasgow, where he is rector, because of his circumstances. It is Universities Scotland, the principals' trades union, that wants to have chairs chosen by the court itself and not by students.

Mr von Prondzynski thought that what's good for Edinburgh should be good for other universities and he's right. The elected rector – like the democratic intellect – represents Scotland's unique contribution to university governance. Any SNP government that tried to abolish rectors would rightly be condemned. Ms Constance has insisted that the Government will not.

Mr Von Prondzynski also recommended that trades unions should be represented on court, so that the views of staff (Edinburgh alone has 20,000) could at least be heard in the governing bodies of the university.

Many university principals were unhappy with the von Prondzynski Report in 2013. They asserted that trades unions had no place in the running of universities. Principals said they also feared “frivolous” rectorial candidates – footballers or comics – chairing court.

But there has been a problem with celebrity rectors for more than a century. It seems somewhat bizarre that universities have only now noticed this, just at the moment the problem is being addressed.

Actually, when I stood for Edinburgh, it was against the Respect MP, George Galloway and the former Labour cabinet minister, Lord George Foulkes; hardly frivolous candidates. I also signed what was called the Rector's Charter. This required me to state that I had no conflicts of interest, understood how the university worked and would discharge the responsibilities of chairing court.

These are not insubstantial. Court met more or less monthly during term on Monday mornings. Late on Friday afternoon a special courier would typically arrive from Edinburgh University with a stack of papers often running to more than 150 pages of documentation from the various sub-committees.

Chairing court really is not for amateurs and, doing a full time job has a political writer, it was virtually impossible for me to do justice to it. Mr von Prondzynski suggested that the rectorship should in future be recognised as a job in its own right, with proper secretarial and research back up and even some sort of remuneration (which could of course be waived).

Cynics have long argued that absentee celebrity rectors actually suit some principals rather well. It is very convenient for some TV presenter to turn up, make a speech and never be heard from again. The court then appoints its own stand-in as chair, which keeps it all in the family.

Most universities are run by a small executive group based around the principal's closest confidants; a kind of privy council. The court, selected from the "great and the good", has often been a passive voice, even a rubber stamp for principals' decisions.

This really isn't any way to run a large public body in the 21st century. Critics of the Bill appear to argue that academic freedom is incompatible with elected chairs of court. But we live in an age of democratic accountability and, in general, it works. Transparency works.

What really lies behind this row is, I suspect, the desire among some university principals that universities should become closed private companies with a management structure similar to a plc. I heard this view repeatedly expressed. There have even been moves to formally re-designate principals as chief executives.

But universities are not private companies. They are public institutions essentially financed by the taxpayer. Parliament has no right to encroach on academic freedom in universities but it has every right to have a say in how they are run.

Many people believe it is unacceptable for university principals to be paying themselves salaries vastly in excess of the First Minister's. There was no formal recommendation on principals' pay in the von Prondzynski report (that really would have brought down the Wrath of Khan). But this pay inflation, modelled on private companies, is corrosive to morale in universities.

And what's wrong with having responsible trades unionists involved in university governance? Why should it be retired bureaucrats and executives co-opted from banks and legal firms who get to sit on university courts?

There has never been the remotest suggestion that the Government of the day should run universities or choose or vet rectorial candidates. However, Mr von Prondzynski took on board the concern among university vice chancellors that rectorial candidates should be prepared to actually do the job, and not just treat it as a vanity appointment like those honorary degrees universities shamefully dish out to celebrities.

The concession made by Mr von Prondzynski was that candidates would have to be interviewed to be certain they understood the responsibilities and were committed to chairing the court. This has been misconstrued by some as “vetting” of rectorial nominees. But the Government has no role here at all.

It did occur to us that university principals themselves might introduce some kind of vetting process and to try to weed out candidates they didn't like.

But if they attempted to do this – veto a rectorial candidate on ideological grounds – it would be a democratic outrage. If you have democratically elected chairs it is up to the voters to decide who stands. It is not for university bosses to decide who is suitable and who isn't.

Sometimes legislation does the reverse of what was originally intended and the drafting of bills is so obscure that it can lead to misinterpretation. But on my reading of this Bill, it seems to be in line with what Mr von Prondzynski called for.

But by all means be critical. We should always read the small print when governments tamper with important institutions. I hope the Bill receives very rigorous scrutiny in Parliament.

There may be some fiendish plot; who knows. Abolishing rectors is not part of it. Critics are only damaging their own case by repeatedly suggesting that it is.