The statement "you will shoot better if you set your variable power scope on its lowest setting" is nonsense.

Now, if you start adding special conditions, then this statement may make some sense. If you are still hunting, you are more liable to quickly locate a running deer in your scope and get a good shot off on this deer with your variable power scope set on its lowest setting. If it is getting dark, you may find that setting your variable power scope on its lowest setting allows you to see better in the darkness.

On the other hand, there are other conditions in which the higher power setting of the variable powered scope would be preferred. This is WHY we have variable power scopes -- because one power setting is NOT ideal for every situation. For example, hunting a pronghorn antelope at 350 yards may be a situation where you would like to use the 9x setting on your scope while hunting deer in the dense Wisconsin woods may be a situation where you would like to use the 3x setting on your scope.

It may be good advice to hunt with your scope set on its lowest power setting and be prepared to crank the power higher when it is needed fora long shot. The thinking here is that you should not be doing any snap-shooting at long range and if you are going to take a long range shot you need some time, and hence you have time to crank the power level higher. If you have a deer at 25 yards you may not have the time to crank the magnification lower or be able to go through the motions -- bring rifle/scope into your lap, crank the power setting over, remount the rifle to your shoulder, shoot -- without spooking the deer.