Step 1: The hallmark histology here is foamy macrophages stuffed with PAS-positive, diastase-resistant material in the intestinal mucosa.
Step 2: This appearance is the textbook finding of Whipple's disease, caused by Tropheryma whipplei, which fills the macrophages with bacterial glycoprotein.
Step 3: Although disseminated Mycobacterium avium in AIDS can also load macrophages with PAS-positive bacilli, those organisms are acid-fast, whereas Whipple's bacilli are not, so acid-fast staining separates the two.
Step 4: Crohn's disease shows non-caseating granulomas, not PAS-positive macrophages. Therefore the classic answer is Whipple's disease.
\[\boxed{\text{Whipple's disease}}\]