Ironically, the Catholic Church had historically operated a not-insignificant percentage of hospitals in the US and around the world. Odds are if there’s a ‘St/Saint’ in the name, it is (or was originally) a Catholic hospital.
This isn’t as new as it appears the joke is implying :/
No offense, but to the uninformed, wet bulb could as easily evoke images of spring flowers in cool spring morning dew.