EMTALA does not apply once the patient has been admitted to the hospital. It applies to ER care only.
There is no medicolegal standard for "life-threatening" That determination is, to a degree, subjective.
In many cases, a patient will come to the ER in a non life threatening clinical state and get sicker following admission. EMTALA no longer applies to these patients.
If, in retrospect, a doctor performs an abortion and its decided that the mother's life was not at risk, they face a felony charge.
Per the Texas Supreme Court, exceptions apply only when death or serious physical impairment is imminent (which is probably too late to save the patient and have a good functional outcome, unfortunately)
The problem here is legislation. There is no medical error. Practitioners are making a risk-benefit assessment and choosing not to martyr themselves.
I feel that you're not familiar with medical practice and are oversimplifying a very complex issue.
I'm going to leave it at this: Doctors and lawyers know more about this than you or I do and it borders on conspiracy peddling to think that not saving a life is being done through simple negligence here.
That particular case needs to be fleshed out in court and may well be an anomaly but there's a reason she is not the only one and the source of that is in the legislature.