All traiing for a licence or rating must be conducted at an ATO
Absolutely, and in the scenario I gave the "PUT" would not be able
to use this flight towards Rating Issue.
All Instructor privileges are written in Part-FCL as privileges to conduct
the required training towards a Licensing Administrative Action.
It does not say you can only conduct training which would, or could,
lead to a Licensing Action.
If this was the case who could give aerobatic instruction to someone
who already holds an Aerobatic rating?
An aerobatic instructor would seem to be the appropriate Instructor
Certificate - but this only gives the privilege to Instruct for the Rating
(not aerobatics in general).