When the need of another person is made plain to us, we can enter into the universal experience of being human, and all distinctions disappear. But we need a humbling power to help us. We need a power greater than our own so that we can adequately relativize whatever authority has been given to us. And the only power that works on the privileged and the underprivileged alike is the divine power of Jesus.
We come at it from different places. Jesus comes to preach good news to the poor and the captive, all the while offering those of us who are not poor, who are not oppressed a place at the table if we can have faith like that of the centurion. However, we have to remember that the faith of the Centurion came at a cost. His faith moved him to an action of humility and letting go of power in the service of another person, that in his day would have been unimaginable.