One of my professors (a viola player) was fond of saying that G-sharp is not in fact the same pitch as A-flat. Then again, he had the luxury of playing an instrument capable of any possible pitch within its range limitations. (Lack of frets will do that to you)

Flute tutor books from the 1720s to the 1860s often have different fingerings for G# and Ab, with G# flatter.

It's easy to do the same on a recorder, and when playing along with a moothie in A, I normally use a fingering that will give a flatter-than-ET G#, since moothies are tuned in some sort of just intonation or meantone.