Back when I played the trumpet (tootle tootle nostalgia!)..erm, my teacher was introducing the idea while I was learning to transpose, Its about playing.. or recognising the key you are in (I think) if you consider that we do not just write F instead of
E-sharp, and so on. So when you change key, keeping the accidentals will sometimes mean you end up with double flats and the like, which are no great leap of the imagination from the E-sharps of the world!.. I think thats all true...