More likely the treadmill is not well calibrated than the GPS is off more than a couple of percent on a medium run.  I've seen treadmills than are off by 10% on pace at running speeds.  Then some (usually cheap ones) are accurate on pace/distance, but just seem to require more effort at the same speed.

If anyone wants to try it, there are two ways to calibrate a treadmill:

1.  Manual:

Measure the length of the belt.  (used a flexible tape measure and slowly sent it through one revolution.

Put a piece of tape on it so you can count revolutions

Run the mill through one minute (or a longer time if you like), at a specific speed, while counting the number of times the tape passes the start point in that time. Make sure it's fully up to speed before starting the count.
# of passes x belt length = measured distance traveled 
Speed (in MPH) x 5280 x time in minutes/60 = Calc. distance (what it should have traveled)
Correction factor = Measured distance/Calc distance.

MPH showing on mill x correction factor = real speed. (so if you're at 7 mph and the correction factor is 1.03, real speed = 7.21mph
Pace showing on mill / Correction Factor = Real pace. So 8:34 pace (=7mph) showing with 1.03 correction = real pace 8:19.

Correction factor may vary with speed , and possibly with/without a runner on the mill. You could test the runner effect at a particular speed, and/or with and without runner.

2.  Garmin Footpod:  Get a footpod for your Garmin, measure cadence and stride length at a steady pace outside, then run on the mill and compare what the Garmin says to what the mill says.  I think that may just bake in any error in the Garmin, but it's quick if you have the pod.