Everybody uses the pivot system, but many of us don't think of it like that. It's all in the head. You can't simply blow the air in the same spot in the mouthpiece for all the notes. But many of us don't think of it as redirecting the air stream, choosing to think of it in other ways, such as adjusting the embouchure to get that note, adjusting the jaw to get that note, adjusting the angle of the mouthpiece on the lips, etc. But as the embouchure gets adjusted one way or another the angle of the air exiting the lips changes.
What's most important is that you have discovered something which helped you play better. Remember it and build on it. Certainly discuss it with your teacher at your next lesson. If it works for you, and truly increases your playing ability and not for just a short term, you should work at it and keep it in your arsenal of playing tricks.
BUT, and it's a big "but" -- you need to work it into your playing so that it doesn't become a matter of forcing you to pause while you make that adjustment. In other words, like your band director said about using one setting. That's not right either -- if if you can play a pianissimo slurred scale from your lowest note to your highest note and incorporate that jaw motion in that scale, then you're all set. If you have to stop the scale and make the adjustment and then continue, then it's not a good thing for you to continue trying to use.
But if Bobby Shew is doing it, it can't be all bad, can it?
