If a situation arises where music has to come second to accuracy, obviously a person would need to do what it takes to get through. But that's when it's time to stop and ask questions so you can avoid putting yourself in quite such an unpleasant and thankless situation again.
As I already wrote, full note accuracy is not the point here. Sometimes it's not a choice between full accuracy and musicality, but the choice between getting through the piece decently or end up not being able to even get through at all. I do not see how it will help someone who already has nerve issues to be publicly humiliated? Assuming this is someone just taking the first steps as a performer, not a seasoned performer. It's true that some people can toughen up after hardships, but as many will end up worse. Telling people they shouldn't perform if they have to compromise on musicality is not something I would expect from a teacher and cannot see how it is helpful to anyone except the really advanced (you are here arguing with amateurs and students, not professionals). It's a great ideal and in theory I would agree, but real life is more complicated than that.
I was having a very interesting lesson with a visiting teacher, who insisted that I play a piece with "feeling" and forget about the notes and details. It is a piece I have worked on for some time and do know quite well. I was not nervous in any way, since it was only a lesson. Unfortunately as soon as I began to play I realized it was one of those days when my muscle memory does not work properly and I also had difficulties to adress the few technical difficulties of this piece because of my hands acting up. When that happens, the only way to keep playing at all is to "toughen up" and use my "crutches" (concentrate on certain details in my mind helping me to remember how to do the more difficult spots). For me hearing the music playing in my head is what I need to play fully musically (which I think is what he meant when he talked about playing with "feeling"). If I need to consciously work on retrieving from my memory details about the next measure or prepare for a fingering, I am unable to keep the music flowing in my head. Multitasking is not one of my strengths. So in those spots my playing will be more dull.
But this time since I was told to do so I tried to just keep listening to the music and play, not thinking so much about the details. I didn't just end up playing a few wrong notes, but could not find my way to the piece again after losing some notes. I ended up stopping and restarting several times in this short 2 page slow piece. But never mind, it was a lesson. It showed me two things: When I do manage to not think about the technical side of playing, I sound better. But it also once again showed me that I do not have such consistency that would make it possible to do that on every occasion or the whole piece.
Should that happen when one is supposed to make a performance should one make the audience (who's expectations are necessarily not that high) suffer with several restarts and messing up the piece or quit after you notice that you won't be able to give it your best? Or just play the piece through as well as you can, even when the musicality is partly compromised? The latter obviously, unless one cares more of one's ideals than for the listeners' comfort.
So if you say one should avoid getting in such situations again, does that mean one should never agree to perform, if one does not know beforehand that one can manage to play freely and musically that day? That's an option as well, but it means only those should perform who does not have such inconsistency as many of us do. And those would usually be professionals with extensive training (or talent enough to enable such consistency with a little less). So much for music making to be for everyone to enjoy
