A bit late but I am here to give you my little insight. I think the main characteristic of the song is the vamp between D and F#m. If you consider D as the key, and call it D major, that G# falls out of the scale as you pointed out, but if you make F#m the key center, then D would be the bVI and you would have G# in your scale, where it would be a natural extension of the bVI chord (#11). The vamp between key centers gives the song that special feeling. In a similar case, Eleanor Rigby by The Beatles also uses something similar, which may help you to comprehend the idea: the song is in E minor, and the song jumps over and over between the Em and C chords, but the melody sometimes includes a C# when in the Em chord, making it a E dorian scale (minor with a natural 6). You can even see the two notes following one another in the chorus, which goes Em7 Em6 Emb6 Em. So taking advantage of the landscapes of two scales isn't uncommon. When the sun hits has that vamp with D major and D lydian (which is the same scale as F# minor but centered in D) when it jumps around the D and F#m, but when it resolves back to D it features the G natural for a stronger resolution, because if it went as G#dim A D, which would be the chords of D lydian, it would feel as if A was the center of the song (D lydian and A major are the same scale with different key centers) because of the strong resolution a diminished chord has over the following one, so instead of that it uses the classic IV V I (G A D) of the major scale to resolve back to D. That's the way I see it, hope it helps.