Although this review article says there is no proof that mushrooms treat disease, it also says that the presence of certain chemicals in mushrooms suggests that secondary metabolites with useful pharmacological properties are widespread in these fungi. I suspect the "no proof" articles were not using them in a way that integrative medicine would, especially since there is good evidence for mushrooms increasing numbers of immune cells.
An extract of Shiitake mushrooms increases the number of various immune cells, as well as the factors that stimulate their growth.
Eating Shitake mushrooms increased immune cells and decreased inflammatory markers
A polyuscaccharide from Shitake mushrooms stimulates the differentiation of immune suppressor cells (T regs) and reverses their immunosuppressive functions, shedding new light on developing novel anti-cancer strategies by targeting immune suppressor cells.
Storing dried mushrooms for a year and a half resulted in a decrease of vitamin D2 to 1/3 or less of their orignal content. But shining ultraviolet light on them can increase the vitamin D2 level.