As it turns out, the rule isn't as bonkers as it sounds. For a short period of time in the early twentieth century parents did, in fact, occasionally attempt to post their children. Although not by stuffing them them into envelopes, as per the "Flat Stanley"-esque image which I bet is now floating around in your head.
The US Postal service came into being in January 1913, and just over a year later the parents of 4 year old May Pierstorff worked out that rather than pay for a train ticket so May could visit her grandparents, it would be cheaper to post her. She wore the stamps (53 cents worth) on her jacket, and travelled in the mail compartment of the train.
A few years later, cousins Josephine McCall and Iris Carter, 7 and 8 years old respectively, were posted to their aunt. Iris cost 70 cents to post, while Josephine was somewhat lighter and cost 51cents. The driver of the delivery truck they travelled in was a Mr W.E. Fawcett. From one of the local newspapers at the time:
"Mr. Fawcett believes that a kid or two at a time to deliver is all right but he is glad the idea does not occur to many parents at present when moving their children and he is dreading the time when he will find children all along the way and persons in parcels at every post office."
