Yes I imagine a social worker would likely advocate for the patient’s care in this case, and yes I believe that would have made a difference. Hospitals want to avoid lawsuits, and it is easier to say “no” to a lone vulnerable individual than it is to say “no” to a trained professional who knows the details of the relevant regulations.

Edit: In addition social workers are skilled at assessing individual’s needs, and in this case may have gotten a more clear picture of what was going on with the woman - such as by offering to call a family member who could have provided additional health information.