All of the above topics were touched upon in an excellent posting by Dr. Steven Novella. You would expect the President of the New England Skeptical Society to be skeptical and he is as he discusses the matter of a nursing home cat whose visits to residents of a certain nursing home are claimed to portend imminent death. An article in the NEJM called national attention to this claim.
One thing to consider in regard to this and similar claims, this would include the famous seizure dogs and weird things happening when the moon is full, is the phenomenon of confirmation bias. A related thought is expressed in the concept of "numerator based"statistics. In Oscar's case the article in the NEJM failed to give us the denominator of interests , i.e. the number of visits made by Oscar to patients' rooms and beds.
Should the NEJM publish stuff like this? It may well have been intended to be a cute (although nursing homes deaths might not be considered the stuff of cuteness) rather whimsical piece of writing and nothing more, but the editors might want to consider how much impact their publication has and that rightly or wrongly folks tend to believe what the NEJM writes.