Sick food workers who can transmit their illness through contact with food should be prevented from working until they are well.

The statement is true because it is essential to maintain food safety and public health by preventing sick food workers from handling food. Certain illnesses can be transmitted through food, especially if a worker exhibits symptoms such as vomiting, diarrhea, or has any communicable disease that can affect food safety.

By keeping sick workers away from food preparation areas, you help to minimize the risk of foodborne illness outbreaks. This precaution is particularly crucial in restaurants and food service establishments where a single infected person can potentially contaminate a large volume of food.

The other options do not adequately address the importance of ensuring that food workers are healthy before they can safely handle food. Allowing them to work under circumstances that may pose a risk to public health, or only considering severe symptoms or manager instructions, does not align with best practices for food safety. Overall, ensuring that sick workers do not return to work until fully recovered is a fundamental principle of food safety protocols in New York City and beyond.