Getting legal advice on the internet can be a risky proposition, and what you are asking effectively boils down to legal advice. That being said, I think it's pretty clear what the overwhelming majority response is. However, what you should really do is ask this question of your supervisor, because if it ever actually does come up in court, "I acted in good faith based on what my supervisor instructed me to do" is a much better defense than "I acted in good faith based on what some people on the internet told me was right".
As long as the person seems, in your judgement, to be physically and mentally able to take care of his or her self, then it should be fine to leave that person alone.
After all, if it's abandonment to leave a person home alone, then once someone goes to a medical facility, they'd never be able to leave. Technically, once the discharge order is signed, the care has ceased, therefore there is no longer a transfer of care to worry about. On these runs, you are just a fancy taxi service. It isn't abandonment for you to leave the person home alone any more than it would be abandonment for an actual taxi driver to leave that person home alone after driving a patient home from a hospital, or any more than it's abandonment for the nurse who wheeled the patient out to the curb in a wheelchair to leave the patient in the "care" of the taxi driver.