You're not most patients. An enormous number of patients--the majority, I'd say--are easily confused. I have seen patients refer to PAs and NPs as the doctor even when they don't introduce themselves that way. I've seen a patient call an anesthesia tech a doctor. I've seen patients call doctors nurses or orderlies.
Most patients are not as well educated as you, and most of them don't understand what the different roles are. Like it or not, the physician is the quarterback. NPs and PAs have an important role, but when you have an NP going to patients and introducing themself as Dr. Lastname, that gets unnecessarily confusing to patients (and their doctors, when the patient says "the doctor" told me X and everyone is trying to figure out who told them that). When a DNP who works in the surgical department introduces herself as Dr. Lastname and tells patients her own opinion on their care, sometimes contradicting their physicians, that is dangerous.