This much is true.
Those duties fall to the Culinary Specialists, the current name for the rate that grew out of the segregated
Cook/Steward ratings of WWII via the Mess Management Specialist rating . They would be the ones assigned to a commanding officer not only to be in charge of the Captain's Mess but also be responsible for the CO's mundanes*, like cleaning his/her cabin, maintaining the wardrobe etc.
A Navy Culinary Specialist responsibilities vary and can include (
source ):
- Menu management.
- Food preparation.
- Mess, kitchen, and dining facilities operations.
- Operation and management of shipboard living quarters.
- Operation of shore-based hotel-type quarters.
- Serve as personal food service specialists in Commanding Officer’s and Admiral’s messes.
- Financial record management.
- Maintain subsistence inventories using storeroom management procedures.
- Provide hospitality and catering services during official command receptions and ceremonies.
- Serve as a flight attendant aircrewman on designated aircraft.
*(Some may object to the servile nature of that but a CO should be focused on his command not on whether he has time to make the dry cleaners before the Admiral's visit.

)