A couple points. 1) When "Believers" was written, Peter's book
hadn't yet hit the stands. 2) Peter likely got his notion of the sick
kid and the religious parents from the same basic source we did: the
headlines. This has been an ongoing problem in real life for some time.
So he took that real premise, and did one story based on it, and we did
another extrapolation. This notion did *not* originate in the Trek