I realize what the value of anecdotal evidence is (read: virtually none), on both sides of the issue. However, we are all colored by our own experiences.
All I can tell you is this: I live in the United States. I have not had health insurance for many years. And health care, including routine preventative, what we call "urgent care," and emergency, has never been denied to me because of my ability to pay. Doctors, urgent care centers, hospitals... all have been willing to work with me as someone who did not have health insurance and could not simply fork over thousands of dollars out of pocket. In some cases, it was by setting up payment plans that I could manage. In other cases, it was by reducing the bill by a substantial amount. On a daily basis, I have to take an extremely expensive medication that the maker, AstraZeneca, provides to me at absolutely no cost because I can't afford it on my own.
In short, I have found the notion of being denied health care in the United States because you can't afford it to be as much of a myth as many of you claim to have found things about 'socialized' systems to be myths.