Final answer:
The most likely causative organism for diarrhea following a meat cookout, with no blood or leukocytes in the stool, is Staphylococcus aureus, which is associated with symptoms arising within a short time after consuming contaminated food, typically one to six hours.
Step-by-step explanation:
The causative organism for this case of diarrhea, beginning 12 hours after eating meat at a cookout and with no blood or leukocytes present in the stool sample, is most likely Staphylococcus aureus. Symptoms of staphylococcal food poisoning commonly appear within one to six hours after ingestion of the contaminated food, which can include meat products.
Stool analysis does not typically show leukocytes or erythrocytes in cases of Staphylococcus aureus enterotoxin-mediated food poisoning. Factors including improper food-handling and insufficient cooking temperatures can lead to the growth of S. aureus and the production of toxins that cause gastrointestinal symptoms like diarrhea.