|Icon of Christ the Healer|
If we take a historiographical approach, we are faced with a serious problem. We lack the evidence we need to verify or disprove the claim. Mark is our oldest, most reliable gospel source. We have no other documents, no evidence closer to the events of Jesus' life than Mark (written probably ca. 70). Secular historians are, of course, highly skeptical about the claim of Jesus' healing powers, partly because it is otherwise undocumented and partly because it does not fit with their understanding of how things work. Historians, however, are in theory supposed to set aside their own values and beliefs, as best they can, in order to get at the facts whatever those facts may be. Truth is, they often don't put aside their own biases, something that is incredibly difficult to do anyway. In this case, all the historian can do is to note that this one source makes this claim. It sounds unlikely, but then many of the things that happened in the past were unlikely—"unlikeliness" alone is not a sufficient cause to discount the data. As unlikely as it seems, it could have happened that (many) people were healed by touching the hem of Jesus' robe. We don't know.
Or, we can take an allegorical approach. The truth of the claim is that if people will come to Christ in faith, Christ will give them healing. The claim then points to the power of God in Christ. It tells us how God acts in our own lives. The story is thus true as it stands and its truth can be tested by putting one's trust in Christ.
A third possibility is to acknowledge, as a matter of reasonable faith, that the claim has an important kernel of historical truth in it, which reflects deeper spiritual truths. Jesus, that is, was a man who accomplished some astonishing things. By whatever means, he healed at least some sick people, enough to make a strong impression. More generally, his charismatic personality made a deep, lasting impression on people, so deep and lasting that claims like this one naturally arose. To this point, we walk a line somewhat similar to that of the secular, unconvinced historian, conceding only that the claim made in the Gospel of Mark may well reflect some historical facts. And then, we walk beyond the skeptical scholar to acknowledge that for followers of Christ something more than "mere facts" is involved. Empirical truth is one form of truth. Truths of the heart and Spirit are another form. Faith in Christ acknowledges that the historical facts are sketchy and unreliable at best, and then says, "Still, I trust." Faith finds something deeply persuasive in the church's witness to the truth about Jesus of Nazareth that transcends the critical historiographical method. Jesus remains a powerful, astonishing, and wise figure in himself, and the embodiment of God's love for us as best we can understand that love.
There are facts, and then there are facts. The critical historical method does not have a corner on the fact market, no matter how much its practitioners would have us think otherwise.