I've never had this discussion before (NP vs MD) but I have had many discussions over proper titles in a customer setting as a microelectronics engineer and in a research setting as a bioengineering scientist/researcher specializing in neurological treatments (nerve regeneration, artificial limbs, genetic alterations, etc). Btw, you often do have patients in a research setting depending on the stage of the trial. Never once have we had the discussion over an earned title. It was typically over less clear situations where the title wasn't specifically earned. PhD, MD, DNP, etc. was irrelevant. The individual always is expected to introduce themselves by their proper title Dr. Xxx. Sometimes more detail is given in title, sometimes not. What is always given is the role being performed. "Hi, I'm Dr. man. I am in charge of Xxx.". The MD, PhD, DNP aspects are not important. Nor should they be. The only thing that's important is their role and responsibility. The title isn't even important, it's just a sign of respect for hard work earned. This was proper behavior regardless of setting patient was being monitored or seen in. The bottom line is that we are expected to have the capability to do our jobs.
I don't expect an MD to have my level of knowledge about neurology or genetics unless he's doing research. I've seen things that an MD would never see in a patient setting without the extra uncontrollable variables to cloud my interpretation of the data. I only expect them to understand the results of my papers and be able to apply them (in regards to providers not involved in research). They don't expect me to have complete knowledge of systemic responses of overall body under those many possible uncontrollable variables. Just like the DNP is expected to have a better understanding of the impact on the patient themselves and overall outcome (holistic) and not just the outcome of their specific conditions as well as the impact on the patients life. In other words, just because a treatment exists, it doesnt mean it will be adhered to or desired by the patient. (Those are all just examples). We all know the disease, the systems affected, and the treatment but our experiences, and therefore perspectives, are different.
In regards to the NP vs MD debate which keeps coming up here, after being involved in this discussion, I'm happy that it's happening (integration of focused system level healthcare provider). The trend is in NPs favor worldwide and research in places which have given NPs the ability to practice are showing consistent positive results from independently practicing NPs. So the argument that they aren't capable has been thoroughly disproved by independent research from what I've read. That said, as far as I'm aware, those NPs all had considerable experience. The only thing I would like see added is an experience requirement that other licensed professions dealing with public safety are required to possess.
Other than that, I think this is good for the field and good for MDs. Not just because it will reduce their load, but because it will lead to more small businesses and more affordable Healthcare which are both good for the economy and society. Also, hopefully it will change the culture I'm seeing in this discussion where people believes their superior or more capable than others based on easily deconstructed arguments. I hope this is primarily an issue with med students and that they grow out of it with experience because I have not noticed this level of superiority complex in any professional.