I have been privileged to study with two recognized artists at times of their fullest artistic and personal maturity. (I studied with two artists in addition to these, but their artistry was not world-renowned, so my point does not apply to them.)
In the first instance I had organ lessons over the course of an academic year in which it was clear that we did not get along: the master was blind and, besides having to communicate in a language I had not mastered, I would arrive at my lessons physically ill from unbearable tension. Toward the end of the year he assigned me analysis of a Prelude and Fugue by Buxtehude, a work that was totally new to me.
His response to my analysis was to ask where I had gotten it from. I was crushed. "It is my work."
He then proceeded to tell me the truth about his teaching of the many foreign students who came to work with him. They expect to be taught in accordance with accepted usage, so that is what he teaches them. When he performed, he told me, he executed the ornaments "correctly" the first time through, but on the repeats he did as he felt the music demanded, which was often in direct contradiction of the learned treatises, and he demonstrated what that entailed.
In confiding this to me he gave me a great gift, much more significant than praise.
The second case involves a master whose work I admired beyond description despite the fact that I often disagreed with it. I tried and tried to emulate it and could not. I had one lesson with him in which he identified clearly and accurately the essence of my piano playing, by so doing giving me hope that one day I would figure it out. It took a while but I did figure it out. And I noticed that, as I did so, my playing was resembling his to an increasing degree.
I cannot state on a resume that I studied with him as I enjoyed only that one encounter, pivotal though it was. But I listened attentively to pianists who have studied with him and find in their work no trace of that teacher's particular voice.
I am reminded continually of the earlier encounter.