By the end of the article, we still don't know what's affecting the girls, but the author is strongly hinting in the direction of a mass pychogenic illness, a.k.a. mass hysteria, which has been a front-runner diagnosis from the beginning (although generally rejected by the victims and their parents).
There's no evidence of environmental contamination. One doctor has come up with a fringe diagnosis, and is treating for it, with some success, but international experts on his diagnosis say it's basically impossible. Oh, and there's a pattern of weak family ties in the homes of the afflicted girls. It ends with some talk of the successes of a doctor who is pursuing psychological therapy as the main treatment (along with exhaustive testing for other causes, just in case).
As he comments, it's hard to distinguish between his treatment and the placebo effect. Given that his treatment is mostly harmless (unless you're a bacterium), does it really matter?
"[...]a Hindu priest (pandit) who asked the Hindu elephant god for help in appeasing the disturbed spirits of [an accidentally partially bulldozed sacred pool near the school playground] during a public Om Shanti ceremony."
from: OUTBREAK! The Encyclopedia of Extraordinary Social Behavior by Hilary Evans and Robert Bartholomew.
http://www.anomalistbooks.com/book.cfm?id=37
I think the key is to be very solemn and convincing, and to either honestly believe you're effecting a cure, or never let on that you're bullshitting.
You thought Victorian English was verbose, ornate, and unnecessarily obscure? Try the modern NYT! Shorter sentences but longer nearly everything else.
The snobbery is jut dripping off every word in that article.