"Medically unexplained physical symptoms (MUPS) are physical symptoms for which no relevant organic pathology can be found. MUPS are very common, comprising up to half of all consultations in primary care and up to one third of those in hospital outpatient clinics.1 Some studies indicate higher prevalence; a landmark study of medical outpatients in North America with new complaints of common symptoms such as chest pain, dyspnoea, dizziness, and headache, found that an organic cause was demonstrated in only 16% of cases.
...Although MUPS are a major clinical problem and widely regarded as being difficult to manage,4 sophisticated approaches to management or even recognition of the problem are unusual, especially in hospital medicine." [1]
I do realize that a case being marked as MUPS is not proven to be psychosomatic (psychological). Yet if even a small amount of MUPS cases are correctly diagnosed, there'd probably be enough of them to surpass the term "rare".
Yes, ideally we would run every possible test on any patient that walks in with a stomachache. But there are limits to our economy and to doctors' time. It's a complex problem.