True. But not totally correct.
What you are saying only applies to flight training beeing made in a flight school towards a licence or rating for which you need an approved flight school.
According to a question I made after the last thread directly to the authority a training flight is a flight that do not need a flight school permit and therefore this rule you quoted does not apply. This rule only applies to school flights that needs an ATO permission. And you can indeed do a training flight without full controls.
Therefore this specific situation.