You get billed, but you can just go home and not pay it. That doesn’t necessarily mean that the issue won’t still be waiting for you if you come back, though. I can imagine a situation where a foreigner left behind substantial medical debt and the State Department refuses to allow them back in. So if you’re a frequent visitor, or need to visit here again in the future, it would be a problem.
A one-time visit? Fuck it. Go home, back to your more civilized country, and leave it behind.