The Very Model of a Modern Miracle Maven

I know this doesn't even count as secondary source but on his blog, Robert Price reviews some apologists' book and includes this line:

Bultmann freely admits that Jesus did what he and his contemporaries regarded as miracles, both of healing and of exorcism. Whatever you may want to make of them, Bultmann said, you have to admit they might have happened because such things, such scenes, occur today.

Whether or not Bultman said this, it is true. We do see faith healings and exorcisms today. Granted James Randi's ilk have shown that they prove illusary or fraudulant upon closer examination but would your average witness/audience member know this at the time? Or later when he is describing the event to a friend?

P.S.: Apologies to the estates of Misters Gilbert and Sullivan