Great observation, Penny, but then I have come to expect that of you. I am not sure, but that would seem to be as good an explanation as any as to how "kidding on the square" and similar sayings came about. The place that I recall hearing this term used on a regular basis was Southie (South Boston, for the uninitiated). This is a heavily Irish Catholic enclave. I wonder if it developed as a tongue in cheek jab at the Masons.