Jung and Freud are not often used as basis for training in therapy, although there are still some who follow the psychoanalytic model. Others like Aaron Beck are considered more relevant.
Psychology as a science addresses different things depending on what type they are. There are several research areas of psychology that engage in research on human behavior but never study clinical matters or see any clients ever. The clinical side of psychology and its line of scientific reasearch looks at mental illness and the efficacy of various treatment modalities.
The patient you just described who "spilled their guts" to a prescriber didn't understand the model. It sounds like the patient in question expected therapy but were at the office of a prescriber (MD, NP, or PA). If they didn't want medication, the prescriber was not the right professional to go to. The person who writes the scripts is not the same professional that provides therapy. Different training entirely. The exception being there are some psychiatrists who do some therapy. But they rarely have full hour sessions and generally do provide prescriptions. A lot of people who write scripts nowadays are NPs or PAs and I don't know how much training they get in therapeutic techniques.
I've had I don't know how many clients ask me to write them a prescription, and are disbelieving or suspicious when I say I do not and cannot.
Or how many clients I've had who complained that "my last therapist was just pushing pills, pushing pills" If the last "therapist" was actually writing scripts, they weren't a therapist, they were a prescriber. (MD, NP, PA)
Therapists are either psychologists (PhDs or the equivalent) or social workers or licensed professional counselors/licensed mental health counselors [me] master's level clinicians. We do not have the training or licensure authority to prescribe medication.
Having said all that, I recognize that all this seems very convoluted to most clients. The system is not streamlined or straightforward at all. The clients don't find these things out ahead of time because they don't know what to ask or whom to ask, and those who refer them don't tell them.