**Core Concept**
The question is testing the student's knowledge of a specific glomerulonephritis associated with skin manifestations and joint involvement. This condition is characterized by the deposition of immune complexes in the glomeruli, leading to inflammation and damage to the kidney tissue.

**Why the Correct Answer is Right**
The clinical presentation of non-blanching rashes (purpura), joint swelling (arthralgia), and hematuria (blood in the urine) is classic for Henoch-Schönlein purpura (HSP), also known as IgA vasculitis. HSP is a form of vasculitis that affects small blood vessels, including those in the kidneys. The presence of IgA immune complexes in the glomeruli is a hallmark of this condition. The renal biopsy specimen would most likely show IgA deposition in the mesangium, leading to mesangial proliferation and glomerulonephritis.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option might represent a different type of glomerulonephritis, such as membranous nephropathy, which is characterized by the deposition of immune complexes on the glomerular basement membrane, but it does not fit the patient's clinical presentation.
* **Option B:** This option might represent a condition such as Goodpasture syndrome, which is characterized by the presence of anti-glomerular basement membrane antibodies, but it does not fit the patient's clinical presentation.
* **Option D:** This option might represent a condition such as lupus nephritis, which is associated with systemic lupus erythematosus, but it does not fit the patient's clinical presentation.

**Clinical Pearl / High-Yield Fact**
HSP is a classic example of a small vessel vasculitis that can affect multiple organs, including the kidneys, skin, joints, and gastrointestinal tract. The presence of IgA deposition in the glomeruli is a diagnostic hallmark of this condition.

**Correct Answer:** C.