If the other G string stays in tune, then the nut or saddle grove for the string that goes outta tune (when you fret the string) is too low.

"String theory"

Take any string and put it under tension. Lightly, find the half-way point of the string. Touch the string and pluck it lightly. It will sound a note that is called a harmonic. Again, half the string from that point to its end point. Again you will sound a note that is a harmonic that is one octave higher than the first note. The frets on guitars are placed the way they are (notice that they get 'closer together' as you move your hand to tward the body of the guitar. Each fret is placed where it is because of the necessity to shorten the string where it will vibrate to fairly exact lengths. Subsequently, I would think the problem is with one of the grooves and not the frets, because the other strings are not giving you the 'outta tune' problem.