I agree with a lot of what volodos says.
Don't practice too much is true. But it depends what he means by practice too much. I always work until I am satisfied with the results. This may take 2 hours, if so I'll stop. It may take 9. I think that is a bit of an empty statement by him, becasue to label any amount of practicing too little or too much is wrong. There should be no set time limit. If you play 8 hours day everyday, it's bound to effect your playing becasue you'll have nothing to express in your music except the 4 walls of a practice room, wheras the person who does 5 hours, and spends 3 hours having a good time, will have a much more balanced personality.
The 2nd statement is in some ways true and in some ways wrong., A teacher is there for guidence. Talented students will do most of the work themselves, the teacher just guides them. Most of the time when lessons go badly, it's becasue the pupil hasn't prepared. In that case what can a teacher say? People take lessons later on in life to get information, and share opinions. Lang Lang was hardly getting a stereotypical lesson off Barenboim, it was more of a musical collaboration.
Piano playing is all from the head. Thats true. The muscles and tendons etc.. work, but they can only be used correctly if the brain know's how. So many techncal problems are solved if you just sit and look at the problem, and solve it. So many people sit and thump away hopin for the fingers to strengthen and the muscles to grow. It's a simple case of thinking what do I need to do? Why are my fingers not doing that? Analsysing hand position, why the tension is there.
Nobody can play piano totally relaxed, it requires tension to strike a key. The thing about relaxation is to release the tension. Muscles are designed for tension. It's the releasing of tension that is important. Of course you will get tired playing piano, no matter how relaxed you are, and thats when muscles come into the equation. Pianists must have strong hands and arms, but they must not rely on them.