Think about what each test contributes in a glomerular disease. Light microscopy shows overall architecture, immunofluorescence shows antibody and complement deposits, and electron microscopy shows the fine structure of the basement membrane and any electron-dense deposits.
Alport's syndrome is a genetic disorder of type IV collagen (alpha-5 chain). The basement membrane is built abnormally, so its layered structure is disturbed. Under EM the glomerular basement membrane looks alternately thin and thick, with the lamina densa split into several layers. This is described as a basket-weave or lamellated pattern, and it is the hallmark that confirms the diagnosis.
The other choices do not depend on EM. Goodpasture's syndrome shows smooth linear staining for IgG along the basement membrane on immunofluorescence, which is its signature. Wegener's granulomatosis and Churg-Strauss syndrome are small-vessel vasculitides identified by ANCA testing and by their light-microscopy picture of necrotizing inflammation, granulomas, or eosinophilia, with little immune deposit on the kidney.
So among the listed conditions, the one where the diagnosis truly rests on the electron microscope is the hereditary collagen defect.
\[\boxed{\text{Alport's syndrome}}\]