So imagine that you were a Shaolin lay disciple. You learned the Wood Ignition Chop from Xuan Ku, making you the elder martial brother of Xiao Feng. Then you start boasting to your hometown neighbors and relatives. Are you allowed to pass on this skill to your child?
Or do you have to bring the kid to Shaolin, then he has to learn those skills through an official channel, and you can only help train him afterwards?
It seems like it is taboo for lay disciplines to directly teach without the new student taking a formal monk teacher first. Otherwise Lin Yuantu could have taught some Shaolin internal power method to his Lin adopted child. Imagine the Lin family with the poor external 72 Bixie Jianfa but backed by orthodox Shaolin internal power, they could put up a better fight against Yu Canghai.
Here is a blatant case of seemingly passing down a skill without permission:
Guo Jing taught Guo Xiang 1 Yang Zhi and she used it against the Shaolin monk who tried to guess her martial arts background. Did Guo Jing have authorization to teach her 1 Yang Zhi?
Would it have been taboo for Guo Xiang to teach 1 Yang Zhi to her Emei school?
What if Guo Xiang taught Divine Finger Snap or Peach Blossom martial arts to the Emei school? Huang Yaoshi is the unconventional type, and I'm sure he would have been very proud of his granddaughter. So instead of those wondrous skills, which include palm skills, sword skills and the Divine Finger Snap being lost, why not let his descendant teach it?