The example of the good Samaritan is not one of 'referred to government'. It was one of personal, self-directed charity and good will.
There is absolutely no involvement of government at all in this parable.
In fact, government, as you are attempting to advance its role, is antithetical to this behavior. In your idealistic world, the good Samaritan would have been legally bound to act in the way he did, and would not have had the sustenance to send the man on his way, supported by his financial charity.