Why is the initial first-line response to a psychological problem not a brain scan?
The first stop when a non-emergency medical issue evolves is, as you say, a visit to the GP. This is not a supplement to diagnosis. Instead, a visit to the GP can be a critical step in the treatment process and a GP will assess what the most probable underlying cause is during a consultation, based on a physical examination and verbal communications. Then the GP can refer the patient to the proper next medical practitioner for specialized help. Note that a diagnosis involves mainly excluding other causes and narrowing down the list of options.

Your case report lacks some critical information (e.g., age at diagnosis etc.), but the statistics behind the diagnosis can still tell a lot about the GPs decision: 


The incidence of brain tumors is about 22 cases per 100,000 individuals (0.02%). Brain tumors are most likely to arise in kids or late teens. Dependent on the age of your friend at the time of diagnosis, this may have placed them out of that age window.
The incidence of visual hallucinations is about 17 per 1000 (1.7%) (Tien, 1991), i.e., orders of magnitude higher than brain tumors. In other words, just a minor fraction of visual hallucinations are caused by brain tumors. A more likely cause for hallucinations are positive psychotic symptoms, the realm of psychotherapists and psychiatrists. Most visual hallucinations are caused by psychosis (e.g., schizophrenia), Parkinson's disease and Alzheimer's disease (source: WebMD). The latter two are typical cheriatric diseases (diseases linked to old age). If your friend was not considered an elderly at the time of diagnosis, it would make psychosis the most likely candidate cause of the symptoms. 


Brain scans do not diagnose Alzheimer's or Parkinson's, nor psychosis. A brain scan would only, perhaps, find a tumor that has a very small chance of occurring. Moreover, a single scan may not be enough. The tumor may be small and clinical tests, fMRI, PET, or bone scans may be necessary (source: JHMI), which can result in an extensive list of scans, many hospital visits, and associated financial burden. The GP chose the best hit, and that's a psychiatric issue.  

Reference
- Tien, Soc Psychiatry Psychiatr Epidemiol (1991); 26(6):287-92