Luke 8:22-25; 40-56
In the 8th chapter of Luke's gospel, we are given an account of several miraculous events. Let's look at 3 of them - the calming of the storm, the healing of a woman, and the healing of Jarius's daughter.
In the first, the disciples wake Jesus up who is sleeping on the boat they're on. They are frightened because of the storm. Jesus calms the storm, and asks them, "Where is your faith?"
In the second, a woman with a long term bleeding pushes through a crowd around Jesus to touch his cloak. Jesus immediately realises this, and asks who touched him. When the woman identifies herself, Jesus replies, "Daughter, your faith has made you well."
Finally, Jesus is asked by Jarius, the ruler, to heal his daughter who is sick. After being distracted by the bleeding woman, someone tells Jarius to leave Jesus alone as the daughter is dead. But Jesus implores them to not fear but, "only believe", and she will be made well. They don't in fact believe, but Jesus heals her anyway.
What's common in these three passages is that they all refer to the faith of those involved. In the calming of the storm and Jarius's daughter, the people don't believe, but Jesus saves nonetheless. In the case of the bleeding woman, she does believe and Jesus says that's what saved her.
Is this passage making a point about whether non Christians can be physically healed by God? I don't think so. It tells us something about faith. Jesus reaches out to us even when we don't believe, to bring us to know him (you can see this in the calming of the storm and Jarius's daughter, where the disciples and the parents are amazed at him after the miracle). But we also see in the case of the bleeding woman that it is faith that saves.
Jesus reaches out to us even when we don't believe, so that we might have faith in Him. And it is through that faith that we are saved.