You know that Jesus drove a Honda, but he didn't like to talk about it - he said, "I do not speak of my own Accord."
You are correct. The program notes from the Kingston Trio album say that the song “Mary Mild” was taken from the “Bitter Withy”.
Quoting:
“Mary Mild, a version of the ballad “The Bitter Withy” is founded on an Oriental legend known in Europe before the end of the 11th century. The story, not found in official church writings, tells of Jesus at the age of eleven being chastized by Mary for building a bridge of sunbeams to illustrate his divine power to neighborhood children who refuse to play with a child so humble born. The “bridge of sunbeams” miracle has been traced from Egypt to Ireland and to the lives of the medieval saints.”
The Kingston Trio version omits the references to switches and spanking.