I was looking back over some of my rounds in the past year.  I was trying to see how GIR related to my score (and differential for handicap).  I was suprised to see that I had some low rounds with low GIR.  FIR is even a less important stat, but I'll stay focused.

The most interesting was a tough course I play in Ohio sometimes called Sugar Valley Country Club 9 (71.9, 128 slope).  I only hit 5 Greens in regulation, but Shot a 79.   I shot a 1 over 36 on the back nine and only hit 2 greens!  

A course I Play a lot at home, Quail Ridge (70.8, 124), is a par 70 course.  I twice have shot a 76 and only hit 7 greens.  One time I shot a 79 and only hit 5 GIR.  

 

I have other examples, but the point is GIR doesn't account for: 

1. Barely missing the green but being close to the pin, or having an easy chip shot.

 

2. Hitting the green but having a difficult 40-70 foot putt.

 

GIR is a decent stat, esp if mixed with putts per GIR.  But proximity to the hole is probably a better isolated stat for accuracy. A lot of people think they need to hit more greens, but a lot of times putting or chipping is the real problem.  Hitting a green in regulation doesn't mean you are accurate.  Most of the time I'd rather miss the green and only be 15 feet from the hole than hit the green and have a 45 foot putt.