My understanding was that "ab initio" that is "from the beginning " was a universal term for initial pilot training and in the private flying context referred to training for the PPL. That is the sense I was using it.
I take your point about many professional pilots also being involved in private flying, and that is in fact the case for myself. My day job is flying a large T Prop airliner but I also own shares in two light aircraft and teach part time so I think I have an appreciation of both sides.
Just because an airline training program does something does not automatically mean it should be adopted at the flying club. For example most airline academies use 2 crew SOPs and CRM from the very first lesson. A great idea if your first post training airplane is an Airbus, not so usefull for renting that C 172 for your first post PPL flight.......