Why? Ireland has longer lifespans and better health-adjusted life expectancies than the UK.
Playing devil's advocate, I guess one could speculatively argue that Ireland's private system* brings up the overall average while the public system only caters to the poor and deprived, but I don't think this would be enough to bring the averages up on its own. I'm sure it's more likely lifestyle factors.
* for those unfamiliar, Ireland has a two-tier health system with extremely poor, underresouced single-payer free healthcare coupled with privately-run hospitals for those with the means to pay.
Sounds like the public system provides the majority of care.
Any "public" system still has a private-tier available to anyone that can afford a plane ticket.
Although, one thing to note is the the government does invest in private hospitals as well, so that 79% figure won't be exclusively public healthcare. This is due to public-private-partnerships whereby a single site will accommodate both a public and private hospital with the entire project being funded by a combination of public and private funds, usually with an extremely favourable arrangement for the private side.
Since we're detailing anecdata, I went on a working holiday to the US and had an accident in work. I was fully covered under my travel insurance, and doubly covered under my employer's insurance. I broke several bones in my hand and needed a costly operation to insert pins. The payment approval time from insurers took longer than the minimum wait for the operation before bones fused. I did not have the operation and have had problems in my right hand since.
I take your point about other European countries doing it better, I'm sure that's true. But the article is using the US system as a metric. I'm living in Ireland and would love to have a system as good as the NHS over here. Everything's relative but when you're comparing the NHS to clearly inferior systems there's not much point playing devil's advocate. There are enough individuals with a vested interest in the disassembly of the NHS as it is.