This is what your hospital system's policy is based upon:
http://www.aaem.org/emtala/index.shtml
They are, in no way, obliged to continue treating or working up a patient once that patient is stabilized. Many do, especially teaching hospitals. But, there is no legal obligation.
For example, an indigent patient comes to your ER because she has a lesion on her breast (using this example because I've seen it firsthand). She is evaluated, and it is determined that this likely represents the "peau d'orange" presentation of an infiltrating carcinoma of the breast. This is not a medical emergency. The patient is discharged with appropriate outpatient follow-up scheduled.
If the hospital was to provide
definitive care, the tumor area would have been biopsied, she would have been admitted for an oncologic work-up including radiographic imaging and tumor staging, this would've been followed by surgery to remove the tumor and/or breast, and then she would've received adjuvant chemoradiation.
That would have been definitive care.
Because the patient can't pay for this service, she is not entitled to it. This is contrary to what a lot of people believe to be the case. Now, if she has medicaid, there is probably a physician and hospital out there willing to provide her care. Would it be the best care, or at least equivalent to the best possible care she could get? Perhaps.
-Dr. Imago
ETA: Sorry, skepitigirl. This is pretty much spot on. And, you address another whole separate problem in the ED... patients malingering to get three squares and a warm bed. But, that's a separate issue that, unfortunately, EMTALA has created a situation that has handcuffed a lot of hospital systems. So, a lot of those patients are triaged, then sit in the waiting room and are watched, especially if their presentation is considered "suspicious" by the triage nurse. If they don't get sicker, they're usually seen much, much, much, much later... unless they decide to leave first.