While what your teacher told you might be true to a point, I'm also fairly certain (even given my limited experience) that there are certain physical traits and characteristics associated with each trumpet that are going to either help you or hinder you in your efforts to match your mental image of what your sound should be. To put it to an extreme, it's like saying you can get the proper lead trumpet sound out of a flugelhorn. While a flugelhorn is a Bb brass instrument, the size and shape of the bell and the mouthpiece that you use make it predisposed to want to resonate in a certain way with a specific type of sound. While the differences between trumpets isn't going to be as radical as the difference between a trumpet and a flugel horn, the question that I still want to ask is why should C trumpets be any different when it comes to the personality and sound characteristics between trumpets? I recently bought a Schilke B6 to play in my rock and roll party band. Why? Because I felt that the smaller, lighter weight horn would be a better match for the sound I was going for than my LB Bach with a 25 bell. It has taken me the better part of a month to get used to the sound and the way that it blows, but everyone in the band agrees that my new sound with the Schilke is better than what I had. Whether this means that you need to go with a more custom or hand built horn is a matter of opinion, but I do think that there are differences in how each and every trumpet sounds. Sometimes the differences are subtle and sometimes they are pronounced depending on the two trumpets in question, but I do think that the differences are there.