Can someone sue a doctor for rejecting them if they don't have health insurance and something happens to them?

First of all, can a doctor reject a patient without health insurance? And if something happens to that person can they sue that doctor?
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I know this to be the case if the patient is in need of "emergency" care and is refused treatment. There was a case in MA a few years ago where a man went to a health clinic complaining of chest pain. The clinic turned him away for lack of insurance and he subsequently died when he would have survived had he received treatment. This clinic was sued and sanctioned by the state including having to change their policies with regards to emergency care. This year it became a law that every citizen in MA must have health insurance.
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