Final answer:
The primary service provided by home health care is the provision of medical care and support in a patient's home.
Step-by-step explanation:
The situation that reflects the primary service provided by home health care is option 3: oxygen being provided in the home and managed by a durable medical equipment company. Home health care services aim to provide medical care and support in a patient's home, allowing them to receive necessary treatments and care while remaining in a familiar and comfortable environment. In this case, the provision of oxygen to the patient's home is a vital service that helps meet their respiratory needs.