I don't know if I agree with your teachers assessment in full but that is to say that the way to being more of a master player has many paths. The one your teacher pointed out is only but one.
For me, it was a progression. I tried playing a guitar a few times during my childhood from 7th grade on but it never stuck until the summer between my Junior and Senior year of High School ('82) when I saw Led Zeps 'The Song Remains the Same' at a theater and then days later saw BB King on Austin City Limits. Knew I wanted to play then, for real.
Worked for my dad during the summer and he bought me a Les Paul.
I practiced regularly and progressed as a player. It wasn't until 5 years or so later that I really got in to hard core playing and practicing. By that, I mean the ability to play where people thought of me as a good player. I practiced all the time by '87.
However, I had to progress to that point. My path was not the same as what your teacher said. By '87, I was the 'pry of from my dead hands' kind of guy but I didn't really fully do that right away. During those first 5 years, I practiced regularly and progressed but it wasn't until '86 or '87 that the switch really kicked in.
Even now, I look at my physical ability to play I had back then and now wondered how I really could do the shred thing as well as I did. I could play fast and clean. Alas, it was constant practice that did it.
So, my deal wasn't an immediate switch that turned on but a growth that found me at a point where I could play what's in my head and my hands did not limit me.
...however, my lack of theory did. Now that I'm older and play as a hobby. That's why I'm here. To learn stuff I avoided back then.
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