The problem is you can´t easily opt back into the public system once you´re out (especially once you´re old), so there are tens of thousands (if not hundreds), that get stuck in the private system without being able to pay the fees because they´ve become poor (possibly because of health reasons), and then they get denied coverage and thus access to medical services.
Immigrants can fall through the cracks in the over-complicated system as well.
The problem is not as insane as in the US, happens "at the fringes", but it still affects thousands and is mostly outside of the perception of society, since everybody just assumes they got the best system in the world.
However, I think we can still say "America's system is totally screwy" and also say "and btw, as a warning, X country seems to be heading down that route too" - I don't think, phrased the way ant6n's post was, it takes away from criticism of America.
Essentially, in a perfect world, nobody would be made bankrupt because they got ill, and it seems right that governments should do everything they can to prevent that. If there is a class of people who get forced into that position because of something they cannot change, then that system is broken - whether or not that broken system adversely affects you personally. For example, the American system is not broken for rich people, and especially those in perfect health. For those people, it works just right.
And even if you are the only person in a country that is given the choice between feeding their family or investigating an abnormal lump, it doesn't matter how many people benefit from the upsides of that system, it doesn't matter if all your neighbours can visit their GP for a weekly checkup without penalty - without a doubt that system is broken and unjust and needs fixing.
But yes, I think most developed-country-based non-Americans would rate America's system as somewhere between "more broken than mine" and "perverse and cruel". The fact that we all use America's system as the yardstick for what a bad system looks like says it all.
Although I recognize the personal hardship this can cause, I fail to accept this as a general injustice. In the German healthcare system nobody is forced to choose a private insurance instead of the public one. Choosing a private insurance when you're allowed to (which often means because you're in a higher income bracket) is usually only cheaper if you're young and healthy. It's basically a gamble on your own health for wealthy people.
And if the wealthy young and healthy population don't contribute to the public health insurance system which also pays for the not-so-wealthy and not-so-healthy (older) population, the public insurance system isn't sustainable.
The real problem with this system is its division in public and private insurance. Mandatory public insurance would mean lower insurance fees for public insurance and the problem of being stuck in private insurance would no longer exist.
So while I get your sentiment you're really arguing against the wrong person here.
Besides that in my opinion there is a significant difference between "falling through the cracks" and making wrong decisions poorer people aren't even allowed to make - and then wanting those poorer people pay for your errors.