^I hear you and understand completely why you would have this view of health care in the United States. We have always been two steps behing Europe and one step behind Canada in terms of the liberalization of recreational drug use. The good thing is though, that in recent years, there has indeed been a liberalization in the treatment of drug addicts. Granted, there is going to be a variation from state to state, but as the so-called epidemic has encroached into the Caucasian population, politicians and concerned parents and citizens have forced the hand.
I've known people who even just ten years ago were prosecuted simply for being in the presence of an OD. It was not uncommon for the cops to try to stick a manslaughter charge on said individuals, automatically implying that because they're the only person there, that they supplied the Heroin. You would be prosecuted for possession of syringes. They would test the barrels for residue of Heroin and prosecute you for Felony possession.
In recent years, what are called Good Samaritan laws have proliferated. These laws absolve individuals from prosecution when calling in an OD. Too many people were being abandoned to die over the fear of dealing with the law. Things have changed significantly and I'll admit that most of my experience is in the fairly liberal bastion of New England, but from what I have learned in research, the rest of the country is following a similar trajectory.
Those who are afraid of prosecution or other negative consequences should absolutely not let this fear prevent them from seeking care, regardless of the law. Luckily, it is highly unlikely that you would be in any trouble whatsoever for seeking medical attention. In modern times, the worst consequence is that the hospital will indeed label you as a drug addict, which, given the fact that all medical records are electronic, could produce some roadblocks in the future if trying to obtain prescriptions for controlled substances.
All of these are no reason not to seek care. The consequences of a missed shot can be and often are much more significant than the minor consequences you will face by seeking medical treatment.