My son contracted Kawasaki Disease in 1987 when he was 4. It was a terrifying experience as the doctors could not explain what was causing his symptoms, including a fever of 104. The poor kid underwent spinal taps and more. Eventually he was transferred to Boston Floating Hospital for Children where they concluded he had Kawasaki. There was no test for it - it's one of those "process of elimination" diagnoses and not all who have KD have all of the symptoms. At that time, there was no known cure but my son was enrolled in a random trial of gamma globulin infusion and, thankfully, the dosage he was assigned turned out to be the one that worked the best. He recovered and tests showed no lasting heart damage.
At the time, there were many wild theories as to what caused it. One of the more prevalent notions was that it was triggered by carpet cleaning chemicals, since debunked. This paper smacks to me of "correlation does not equal causation". I'm especially dubious about the supposed geographic origins given that incidents, while clustered around metropolitan areas, were not confined to the west US coast (we live in New Hampshire.)
Over the years I have read many articles and research papers about Kawasaki Disease. I don't think we're any closer to an explanation than we were in 1987.