I'm going to have to agree with Brian here. This is about as good an explanation as I've seen as to why he's right. Dogman, forget about forward and backward arm swings 'canceling out' each other; they actually don't matter at all unless you're moving very, very slowly.
If the Garmin GPS units were actually able to continuously track your position, then yeah, arm swing would come into play. The GPS unit would show that you traveled a lot farther than you actually had because it would show your arm swings as forward and backward movement, essentially doubling your distance travelled. BUT - the Garmins only track your position at certain intervals (about every 4-5 seconds on average I think), so all that matters is where the unit is located at that very instant the GPS records your position. As Brian pointed out, as long as you are moving fast enough so that each tracking point is further along the route than the previous tracking point, arm swing has only an extremely tiny effect on accuracy.
Here's an illustration: let's assume you've set up the Garmin to track your position every second. Let's say that you're walking slowly at a constant speed of 4 feet per second. For simple math, assume that you're swinging your arm 1 foot behind/ahead of your torso on the backswing/frontswing. You start the watch as you begin walking, which records your begining point - A. One second later, the GPS records your position again - B. Let's say your position was recorded when your arm was at the forward-most part of the forward swing. So the GPS will say you've traveled 5 feet, when in reality you've only gone 4 feet. Another second later, the GPS records your new position - point C. This time, you were at the back of your backswing, so the GPS shows you've traveled 7 feet total, when you've actually gone 8 feet.
You can keep walking as long as you like, but the GPS is never going to be more than 1 foot off in total distance. Sure, the individual "splits" or distances between tracking points will vary slightly; they will all be between 2 and 6 feet (assuming the specs mentioned above), when they should all be exactly 4 feet. But the TOTAL distance will only be off by 1 foot, at most.
Again, if the GPS tracked your position CONTINUOUSLY, Dogman would be right. But this doesn't happen at all - the GPS only records INSTANTANEOUS position at certain intervals. It doesn't at all matter what movement goes on between each interval. You could be zig-zagging left and right between each tracking point, but the GPS would still show your movement as a straight line. The only way arm-swing would in any way affect the accuracy would be if you were moving so slowly that your forward arm-swing at tracking point "A" was AHEAD OF your backward arm-swing at tracking point "B."