To me the discussion whether the story is true or not is kind of irrelevant. Instead I would concentrate on the need of using common sense when travelling. When doing strange things like sleeping in a tent in Harlem with valuables (sleeping in remore areas in LatAm is probably "safer"), one never should his wealth, travel without insurance etc. It seems that unfortunately they have done more or less everything that Lonely Planet tells that one is not supposed to do to reduce or the risk of getting robbed will skyrocket regardless of destination.

Anyway, AA might waive the change fee if they have medical certificate proving the need of immediate repatriation (and proving that they are fit to fly). If not, the parents can pay the change fee with CC on the phone...