Yeah, the knee-jerk response should not be "the correlation is spurious", rather it should be "the causation is different from what the authors would like it to be". (That is, whatever hypothesis they came up with, we should assume it's wrong and tell the authors to go pound sand unless they provide strong evidence otherwise.)

In this case, as others are saying, the explanation that comes to my mind is: "What kind of person gets vaccinated against rare diseases that people don't normally get? Probably one who cares extra about health and has resources to spend on it, and has a proactive and vigilant doctor." Selection bias should always be considered in correlational studies.