Step 1: Picture the disease process.
A stone blocks the kidney for a long time. Bacteria keep attacking the blocked kidney. Instead of healing, the kidney tissue turns into pus filled, fat laden nodules. This slow destructive process is xanthogranulomatous pyelonephritis.
Step 2: Match the age and setting.
XGP is seen most in middle aged to older women and men with a history of recurrent UTI and stone disease, which fits a 65 year old with fever and flank pain.
Step 3: Explain the imaging clue.
The "fat densities" on the scan come from lipid filled macrophages (foam cells) that replace normal kidney tissue. No other option on this list produces fat density change around a stone.
Step 4: Eliminate the rest.
A simple renal abscess is a walled off pus pocket, not fat replacement. Chronic pyelonephritis gives scarring and shrinkage. Tuberculous kidney gives caseation and calcification, sometimes autonephrectomy, but not fat density change.
Step 5: State the answer.
The combination of fever, flank pain, and a stone with fat density confirms the diagnosis.
\[ \boxed{\text{Xanthogranulomatous pyelonephritis}} \]