If I'm flying with a student, then they are 'under' my RT licence, same for a solo student.
That's not strictly true.
Art 46 (1) The radio station in an aircraft shall not be operated ... by a person duly licensed or otherwise permitted to operate the radio station under that law.
which is why Art 21(2)(a) quoted by Mike Cross is required.
There is no similar prohibition on operating the flight controls. However, 21(2)(c) allows a student undergoing dual instruction to
act as pilot. Without it, the student would not be allowed to log the time.