Afraid that's not true. Around 60-80% of diagnoses in primary care settings are made purely on the basis of the patient history (followed by a brief clinical examination which usually aims at eliciting subjective responses)[1]. In principle it's true that you could find a pathological explanation for all somatic ("physical") diseases which in practice are diagnosed off patient histories (with the exception of diseases for which the pathogenesis is unknown, f.ex. fibromyalgia, IBS, CFS, etc). However - in principle - the same goes for mental illnesses, although the pathogenesis of mental illnesses are generally poorly understood. If you don't think there's a physical basis for mental illnesses though, skim through the figures in this article[2] for a prime example of the ways modern medicine is disproving that. Diagnoses of both mental and somatic illnesses are heavily based off subjective factors, and both mental and somatic illnesses have very real pathophysiological etiologies.
[1] Source: medical school. Not finding a study with exact numbers from a quick search. [2] https://www.nature.com/nm/journal/v23/n1/full/nm.4246.html