No he (or she) doesn’t, AOTW, if the HOO is the HOO of an organisation which has no legally binding relationship with (in my example) the instructors delivering flying training at one of APTA’s ‘Alliance’ ‘members. Please read what I’ve posted a few posts ago.
You can give it a go. Explain to me how APTA gets a ‘rogue’ instructor or CFI under control at ‘Alliance’ ‘member’ X, when APTA has no legally binding agreement with either the instructor or CFI. And I reiterate: Baseball bats and cement shoes and holding one’s breath and stamping one’s feet until one’s face turns blue don’t count as legal or effective means of control.