Should a nurse or physician istant call themselves a doctor if...?

Absolutely not. In the clinical setting a "doctor" is an MD or DO, or in sub-specialties could be a dentist, podiatrist, or optometrist. Chiropractors, as well, in their own practice can call themselves doctor. A PA or an NP do many of the same things as doctors, but they are not the same. Even having a doctoral degree in something else, doesn't matter. Calling myself doctor would confuse the patients and might be considered mis-representing myself, which in many states can get your license revoked. If you want to be called doctor, go to a 4-yr medical school.