Final answer:
The structure closest to and covering the renal cortex superficially is the renal capsule, which is the innermost layer surrounding the kidneys.
Step-by-step explanation:
The fibrous structure covering the kidney that lies in closest proximity and superficial to the renal cortex is the renal capsule. This is the third and innermost protective layer that surrounds the kidneys. According to the anatomy of the kidney, the renal capsule is just above the cortex and helps protect the kidney by forming a barrier against trauma and infection. Externally, beyond the renal capsule, there are two more layers: the perirenal fat capsule which provides cushioning, and the renal fascia, a tough connective tissue that acts as an anchor for the kidneys.