Exactly this. I currently have four altos, a Yanagisawa, a student Yamaha/Vito, a 1920s Buescher and a Grafton. Using the same mouthpiece, on all of them, I sound like me. When I am playing, I can hear some difference in tone, but objectively, using a high quality recording, they sound so similar, that although I can just about tell which is the Grafton and Yamaha, working out whether I am playing the Yanagisawa or Buescher is nigh on impossible. Someone with a vested interest in a given style or brand of saxes may well argue their products sound is unique, but this isn't borne out in reality.