@David Lieder

my best reason as to why this works, based on my limited music theory knowledge...

start with C major and A minor as examples... they are the same notes, but while I IV V in C is common, i iv v in Am is not. usually, the v is replaced with a V. this is b/c the v is not very strong, and the V chord is responsible for creating the tension that wants to resolve back to the root, I or i. the V7 is often used. now, move this i iv V back to a C major perspective. the i iv V becomes vi ii III.

this raising of the v to a V is why the natural minor scale becomes the harmonic minor scale (7#) and the melodic minor scale (6#, 7#) just evens out the gap created between the 6 and 7 from 3 half steps back to 2.

so the v -> V in the minor scale results in a iii -> III in the major scale. so the G# major works b/c it is part of the harmonic minor scale that is related to the song's major scale.

perhaps @Jim Mrvos has a better explanation.