Student pilots learning in aircraft On Condition??

[Level Attitude]

My understanding is that it is nothing to do with Training per se, but rather
the "commercial" operation of the aircraft - although it has the same effect.

A member of a Group owned aircraft would be paying the Group for use
of the aircraft and, probably, the instructor.
The CAA have given exemptions to this - but not for ab-initio training.

The sole owner of an aircraft does not pay anyone else for the use of their
aircraft. So they could be taught to fly in it (provided the Instructor works
for free?)