Based on the facts details in the post, it is at least arguable that the conversation between the NP and the doctor was merely a consultation on a diagnosis, which medical professionals do among themselves all the time, and not an actual denial of service.
Simon, the NP, described the symptoms to Dinter, the MD, and he gave his opinion -- which turned out to be a really bad opinion with deadly consequences.
But I think it could be argued that it is ultimately the responsibility of the NP or doc who is actually treating the patient, not any physician she might have consulted (and especially not one who has not actually seen the patient), to recognize when she's being given horrible advice. And it seems as if she did recognize that it was horrible advice, but wasn't willing to overrule it and send the patient to the ER against Dinter's advice.
The post says that Dinter implied, during his conversation with Simon, that it would be pointless to admit the patient. But does that mean he _refused_ to admit her? It seems to me that there's at least arguably a difference between the two, and that his conduct did not actually constitute a refusal of service.