Diane you are correct. Many hospitals, particularly those with ERs, cannot refuse patients simply because they have medicaid (or no insurance at all). There are, however, hospitals that do not have ERs - these are likely the types of private hospitals that I was referring to in my earlier post. It would only be these "private" hospitals (and even some of them also have ERs) that could potentially turn a patient away and even then, it's not as if there isn't another hospital that patient could go to - just as you said, any hospital with an ER must treat a patient who comes into that ER. Admitting the patient as opposed to treating and releasing is another story. If the hospital refused to admit, the patient would be transported to another hospital. And though I do not have the statistical data to support it, my guess is that fancy private hospitals with or without ERs probably don't admit uninsured patients or those with medicaid (which does not pay well, by the way - at least not in my state).
This is one of the reasons there are public hospitals. I think of it like education - there are private schools you can pay to put your kids in and there are public schools for those who can't afford or don't want to pay for private education. But an education is required to be made available to all children of a certain age group. A public school cannot refuse to admit a less affluent student, just as a public hospital cannot refuse to admit a patient that needs to be admitted, regardless of whether or not they have insurance or are more or less likely to contract a secondary illness - which would be a highly subjective determination anyway.