This is a popular misconception. In fact, Freud was a "real" doctor who studied neuroscience in medical school and had a career as a doctor working in hospitals. The most interesting thing about psychoanalysis is that it was invented by neurologists like Freud and his mentors Jean-Martin Charcot and Josef Breuer, not by psychologists. The "talking cure" was originally used to cure people who had been hospitalized with various physical symptoms and ailments.
The popular myth holds that psychoanalysis is a non-science trying to mimic science, but in reality it is the other direction. It was originally closer to biology and moved away from that.