Terrible news, isn't it, that the NHS loses £5bn a year through fraud; just awful … to think that people would steal from the public institution we all claim to be so in love with.

But like so many fables of recent history – do people really breed for the child benefit?; do foreigners really leave their homes and friends and everything they know just to come and leech off our unemployment benefits, thinking, "I hope I get cancer, that way I can really max out my EU entitlements"? – we can file this under "It would be terrible, if it were true".

The independent fact-checking organisation Full Fact took a restrained approach to this data, which was presented on Panorama earlier this week: it merely said we couldn't know from the evidence we have whether this figure is correct. We have data covering bent dentists (or "bentists" as this report tragically never calls them) and we have evidence of fraud related to patient charges, and the two figures combined amount to £229m (it sounds like a lot, but as a proportion of the NHS's annual £100bn budget, isn't). It's also a long way from £5bn.

If you want to talk about fraud across government, the greatest losses by a mile are through tax fraud and procurement, our overall lesson is, don't tangle with rich people or the private sector, unless you want to lose your shirt. But let's worry about that some other time.

So where on earth did the £5bn figure come from? Roy Lilley, health policy analyst and a former chairman of an NHS trust, says: "They took a lot of data from a lot of other countries, over a very long period, crashed it all together, and then said, 'This is the average percentage lost through fraud – if the NHS is average, then this is how much they lose'." Even taking an average like that was methodologically flawed – the sample was small and the range was huge, running from 0.6% in one country to more than 15% in another.

Assuming the NHS to be average is unreasonable – our healthcare is (altogether now) free at the point of use. There simply aren't as many transactions within it, as there are in an insurance-based system, for fraud to creep into. And why should the NHS accept a decision by an accountancy firm that they are probably average, and being average they probably lose an average – which is to say outrageous – amount of money? They could reasonably turn around and say: "We're not average, we're excellent. We are first or second in the world on most metrics."

What possessed Panorama to run something on such weak evidence? Has it had its budgets cut? Does it have an anti-NHS mole at the highest level? Someone should do a Panorama into what's going on at Panorama. Or it might be easier just to collate an average competency of investigative journalists across six countries and 20 years and put them in the middle of it. See how they like it.

This government has denigrated the NHS so persistently that I find it impossible to believe it didn't have a hand in these trumped-up fraud claims, yet simultaneously it's relatively easy to believe that it has poisoned the well against the health service so effectively that conspiracy is unnecessary. The anti-NHS mood music has been set; now it can stand back and let that other (once loved) public institution, the BBC, do the work for them.

If you pan out from this story you will see that it's part of the new landscape in which fraud is everywhere and everyone is out for whatever they can get. Councils are so fleeced by benefits' claimants that they have to install lie detector software on their phone systems (not because it works, but to send a message). Outsourcing is a quagmire in which alleged dishonesty – charging the Ministry of Justice for tagging prisoners who don't exist, for instance – is nominally penalised, then rewarded with fresh contracts.

In the rare event there is no scope for fraud, public systems are managed so badly that you'd be doing them a favour to steal from them, just to put them out of their misery. Student fees tripled and yet the government found a way not to make any more money out of it. "We just got it wrong," it says, with a metaphorical shrug, and maybe a literal one too.

You find yourself, if you pay even modest attention, thinking: "What is the point of all this?" And that's the point: to make public services look like an impossible dream, yesterday's utopia.

I was raised under governments that would put out their own eyes before they would admit to having mismanaged anything, or admit any weakness in the way their institutions were run. It has been a difficult adjustment to make, to one that actively seeks to undermine its institutions, blows its own whistle, admit its own error.

It looks like honesty, but it's not. The results of this hand-wringing can be traced most clearly in the university story: they admitted error just as a prelude to the claim that the whole sorry business is now unaffordable. Will fees have to go up? They can't rule it out. Is this the end of a fees cap altogether? You might think that, they couldn't possibly comment (until after the election). If they had come out fighting, we could have fought back; coming out crawling, whimpering at their own inadequacy, all we can do is accept that they've done their best.

Except that I don't believe it. I don't believe that everyone's bent or incompetent. I don't believe our institutions are unviable. I just think we've got the wrong people in charge.