Just gave “Dorothea’s Studio" a listen. The "distortion" on Lloyd's sax, that spitty, crackly sound is common to saxophones when played quietly. There was a thread some years ago wondering about the same sound on "So What" from "Kind of Blue". It can be heard on both Coltrane's and Adderley's saxophones. I think it may also be an artifact of close microphone placement. It does sound quite a bit like common forms of distortion.
I have a nephew who is a budding audiophile. As he has improved his system to be more resolving he wondered about the same sounds. I would put this type of sound in the same category as a guitar player's fingers sliding on strings and piano stools creaking.