This is what folklorists call a "fict" - a term invented by the famed Swedish folklorist Carl Wilhelm von Sydow (1878-1952). The term refers to a type of legends that adults tell to children to be believed, but which the adults do not believe (today, these include Santa Claus and the tooth fairy). Given the absurd nature of the stork tradition, it may have simply functioned as a way to tell suspicious children that the circumstance of birth was not a subject adults wanted to discuss.

Here is an excerpt from my Introduction to folklore dealing with this tradition:

Extensive taboos and actions were needed in the minds of the European peasant to ensure a problem-free birth and to protect the well-being of mother and infant. During labor, locks needed to be unlocked, knots untied, and peas boiled, all in an attempt to reverse the effect that such objects might have in restricting the birth canal.

One common practice related to childbirth resulted in a traditional fict of western culture. A woman was in jeopardy during birth because a host of supernatural creatures might attempt to abduct her and leave a replica in her place that would appear to be her corpse. To avoid such a fate, people ushered children outside and sealed the house. When the birth was complete, the doors and windows could be reopened and the children returned. There was a need, however, to explain the arrival of the infant.

Parents wanting to avoid the topic of conception and childbirth relied on the fact that the only opening to the house was the chimney. Coincidentally, European peasants had observed that storks nested on the little-used gallows or “Catherine” wheel in towns. These looked like wagon wheels positioned horizontally on tall poles, and storks found them a safe place to nest. The birds were regarded as good luck, so it was not uncommon for people to construct a similar wheel on top of their roofs to attract storks. When children asked about the origin of the infant, it was easy to suggest that it had arrived by way of the chimney and that the stork had accomplished this deed.