I know of no Nurse Practitioners nor any form of nurse who may prescribe medication without a doctors approval. I do know of the same who prescribe on something like a blanket approval, meaning that the overseeing physician gives them permission to write prescriptions within a certain range.
One of my friends is under the care of a psychologist at a clinic, and on medication prescribed by the rarely seen Psychiatrist, but he sees a Nurse Practitioner to discuss and change the medication as needed and to re-up the prescription. Any major changes, like getting tranquilizers, require the NP to get the MDs approval. 99% of the time, the Dr just tells him to use his judgment, but now and then, he wants more information and may deny the new medication.
All psychologists that I am familiar with have taken psychiatric theory in college, then studied the various forms of applied therapy, from Reality to Group, and the works of predominate psychiatrists. A 2 year psychologist is basically a social worker, but most in practice by themselves or associated with a clinic have 4 year degrees. Masters, Bachelors or whatever. They select, after the first year, the form of theory they wish to practice then pursue it, or a combination of many. A qualified psychologist is one who knows and uses many theories and they are trained in patient contact.
Facing patients is a requirement for going into general practice because their professors know that all classroom theory is useless if the student in unable to interact with real people. All degreed psychologists are also run through psychiatric tests themselves, first for actual experience and secondly to weed out those who subconsciously are seeking to understand and cure hidden problems of their own.
It is not a good idea to send a trained psychologist out to deal with patients when he might project his own problems unwittingly onto them and apply the wrong therapy. They do find quite a few students who need psychiatric treatment before being given their degrees.
Most psychologists and psychiatrists that I know agree with a combined therapy policy, in that medication must be reinforced with therapy. You will find the medication only policy, applied after a few sessions, mainly in areas where clinics or psychiatrists treat the poor public and are reimbursed by the Government. The low level of payment by Medicare/Medicaid discourages them from spending expensive time with a patient, so does the case loads.
Doctors often prescribe antidepressants without suggesting any visits to psychiatrists. This might work in mild depression or anxiety problems, but not for more serious conditions. Then again, a medical doctor studies mainly your body, and very little of your mind. Thanks to the big budget cuts in mental health in the late 70s by the government, the big progressive boom in psychiatry has all but stalled.
The grants and loans and budgets have not even come close to being fully restored even now and the government is closing State psychiatric facilities. Some great, progressive previously private institutions that lost funds and grants had to join the State, which has archaic rules about therapy and restricts new ideas. In the private sector, due to the major increase in personal wealth, new concepts and ideas flourish but treatment is expensive and the price of the drugs have soared.