I believe your teacher is very right, you must learn to use the base joint of the thumb, this is the proper basic technique. I also agree a lot for the suggestion of a rest stroke - though not common it will be a good base exercise to you and I think this is mostly the reason for this practice.
Later, at complex repertoire the other two joints come to play at times. For instance, at the fast part ( about at the middle ) of Villa lobos etude 11, the thumb plays all 3 basses at one shot repeatedly and there is an also an upcoming arpeggio at the trebles for i-m-a. I have found myself having to use mostly the 3rd thumb joint to accomplish that ( maybe not the best according to the next paragraph ) , as the right hand has to be as stable as possible for the upcoming i-m-a.
I have also noticed what top-players on youtube on that part: I have seen cases where
1) no joint moves (only right hand motion for thumb to play),
2) base joint moves ( most of the players ),
3) second joint moves .
Add to that that I also noticed some right hand movement at 2 and 3 cases, more or less depending on the player. So what I notice from this example is that it is also a matter of personal preference, though the most common between the players looks again to be the base joint