Once again, the president of the United States has elevated a segment on an early morning cable news show into an international diplomatic incident. This time, the subject of the row is the state of the UK’s health service, with a Fox & Friends segment – featuring everyone’s favourite seven-time failed parliamentary candidate, Nigel Farage, as its guest – suggesting the system was on the brink of collapse. Farage said that immigration is the cause.

In a tweet which followed shortly after the news segment, Donald Trump wrote: “The Democrats are pushing for Universal Healthcare while thousands of people are marching in the UK because their U system is going broke and not working. Dems want to greatly raise taxes for really bad and non-personal medical care. No thanks!”

If Trump is going to ignore the huge governmental information apparatus at his command in favour of a news show, it’s a pity he’s picked one that gets so little right – especially as it’s not hard to set out what’s really going on with the UK health system, and how it compares with America’s.

The first thing that Americans should know about the National Health Service is that it’s free at the point of use to anyone who needs it. You don’t have to fill out much paperwork, and you get no bills, whether you go to see your family doctor, or go to hospital. No one in the UK goes bankrupt through medical costs, no one needs to delay medical treatment until they can afford it, and virtually no one is uninsured.

The healthcare it provides is … OK. This is a controversial assessment in the UK, as the NHS often ranks as the most popular institution in the UK, more popular than the military and even the royal family, with nurses and doctors being the two most trusted professions in the country.

Despite its popularity, though, the NHS performs roughly mid-table in terms of bang for its buck: some countries spending roughly the same on health get considerably better outcomes, others get much worse. One country the UK outstrips by a huge amount, though, is the US.

According to data gathered by the OECD, the average UK spend per head on healthcare is $4,192 (£2,989) – and it has a life expectancy of 81.6 years. The US spends more than twice this amount, $9,892 – far more than any other country in the world – and yet life expectancy is far lower.

What’s maybe the most staggering fact is that the US government spends more money on healthcare than the UK government does, despite the latter managing to offer a comprehensive, single-payer health system for the price. The total is $4,860 per person – that’s more than the UK’s total health budget, and $1,500 a head more than the UK government spends.

The reason US healthcare costs so much is its immense complexity: hospitals charge insurers as much as they can, doctors are used to prescribing expensive tests and drugs, and the whole system is so complicated that huge swathes of funding go on administrating the whole mess.

What, then, of the claims that the UK health system is in crisis? It’s true that thousands of people took to the streets over the weekend – on a march to try to protect an institution they care about a great deal. The marchers were certainly not protesting the effect of immigration on the NHS, as Farage dishonestly claimed when the president was likely watching at home: in fact, the NHS is hugely reliant on immigrant doctors and nurses to provide the care it does. Of the NHS’s 1.1 million staff, 138,000 are immigrants – a figure which doesn’t include many immigrants and their children who have taken British citizenship.

Even the UK health secretary, Jeremy Hunt – the target of many of the marchers’ ire, for presiding over NHS underfunding – rose to defend the NHS against Trump’s attack, in rare public criticism of the US president from a serving cabinet minister. “I may disagree with claims made on that march, but not ONE of them wants to live in a system where 28m people have no cover,” he tweeted. “NHS may have challenges but I’m proud to be from the country that invented universal coverage – where all get care no matter the size of their bank balance”.

In reality, the UK is facing the same challenges as many other developed countries: as people live longer and have fewer children, the population is aging, and older people are requiring much more and more expensive care than they used to, increasing pressures on the system.

The government – motivated by a political “austerity” agenda to cut public spending – have not increased NHS funding to keep up with these pressures, leaving the service stretched thin, a situation brought to a head by an unusually severe flu season. Do remember, though, that NHS funding could be increased by 50% and UK government spending from health would still only just be hitting US levels – this is not a system that is intrinsically broken, just one that’s underfunded.

To look for a fundamentally broken healthcare system, Trump need not look very far: he presides over one – and the only actions Republicans have taken during the first year of Trump’s presidency have made that bad system worse.

The US healthcare system is one which is bloated, ludicrously expensive, ruinous to many of its citizens, and leaves tens of millions of them totally unprotected against sickness or injury. Luckily for Trump, though, he’ll never have to sit through a segment saying that on Fox & Friends.

• James Ball is a freelance journalist and author of Post-Truth