Having a good teacher is very important...i've learnt that from yrs of experience.
However once a student reaches or attains a certain level it is important that the teacher has a good grand piano at home to teach the student with. That is what my canada teacher believes.
If the student's parents can afford a good grand once the student reaches an advanced level and the student is serious it is highly reccomended too!
I can feel the difference myself. When I 1st started out for my 1st 14 yrs I practiced on a old Ellington upright(by Yamaha) that never stayed in tune. After moving to canada for about 4 months while I was living at my uncle's house, My parents bought me a 50 yr old Heinzman baby grand(not the new ones, but the old Heinzman made in Toronto). It made a great difference, but unfortunately I did not improve as much as I could because I had to share the piano with my 3 cousins and could'nt practice alot. When I moved into my own home(with my mom&bro, eventually my dad) the home had a 12 yr old K.Kawai KG-2E that the owner wanted to sell as well. After moving into my own home, I improved vastly again, besides that, this piano was my very own to play on as much as I liked, I had it for 4 yrs in total. After going to my friend's(who is now my best friend's) home I took a fancy to his Boston GP-178 which was the 1st Boston that I liked.
Well...I am very fortunate now, after playing and using so many old pianos for years, I have my own Boston GP-178. It has made such a big difference in my playing. Having a piano that I love motivates me to work and I don't take it as work, I enjoy it!
It suprises me too, how practicing on a better quality grand with good keys(that are heavy naturally) makes it so easy for me to play on Yamaha, Kawai, Steinway, Petrof grands etc. My schoolmates often complain how heavy and hard the Yamahas&Kawai's in school are to play, whereas too me, it's nothing, I can adjust to playing on any piano(partly because of the diff pianos I've practiced on for years too)