I do think that this question had a part to play in why I am so convinced that no one can play an instrument exactly the way someone else does. We often are taught that we want to sound like the "greats" of our respective instruments. While it's wonderful to have great role models to look up to and learn from, I find that we often interpret this idea as, "I need to sound exactly like them to be successful."
The truth is, though, we can't ever sound like them, no matter how professional we become. I really thought this question, "Wait, can I play that?" would go away by the time I became a professional, and it didn't. What I found, however, was that I could play the piece in question, but I could never make it sound exactly like the person I was comparing myself to.
That's what made me realize that perhaps we can never sound like someone else because of the simple fact that we are not them. We don't have the same bodies. We don't have the same minds. It'd be silly to assume that all these different bodies and different minds can make the same instrument sound the exact same.
And besides, how boring would that be?
So for now, I'm contenting myself with the fact that at least I know that it's actually physically impossible to sound just like someone else and giving myself permission to not compare myself too harshly with others. Instead, I have room to admire other people's style of playing.
It really makes for a much more interesting world. :)