Angel from montgomery key

[two steps too many]

If it is indeed in G, shouldn't the F(in chorus) be a F#??

It would make sense, acorrding to key charts, that the key of F would be the key that has all the right chords in it, no?

Obviously in the key of G the chord progression is more the typical 1-4-5 type, but then what do you call the F when it should be a F#??

I know there are no rules and such, but I'm just trying to understand more how other musicians arrange their music, and the thoughts and theory behind their choices.

Thanks