I haven't lived in another country, but I have never had an issue with healthcare in the USA. It does seem like you can step on a landmine if you are negligent, but I have employer paid healthcare now and it works great. When I was low income (during my early 20s) medicaid would legitimately hound me to keep me on it. I actually had an issue because they kept enrolling me after I got I job that no longer required them.
I imagine medicaid funding is directly tied to the enrollment count so they are very aggressive about getting people on it. Granted it was trash insurance and most specialists wouldn't take it, but it covered basic care fully.