Yes, I think you are 100% right. On the sax large jumps are super hard because there are so many modes of resonance to choose from and they all 'work' to some extent. If the instrument already has a strong preference for one such mode you can hit it flawlessly no matter where you come from. > 1 octave jumps on the sax were always hard for me no matter how much I practiced especially when going up I kept getting the weirdest (and sometimes pleasant but hard to reproduce) sound effects!