I hear and read about insulin completely unrelated to diabetes pretty often. Just like you said, insulin is responsible for both storing fat onto the body and for helping the body build muscle, but the balance between storing too much fat from too much insulin when you're trying to build muscle instead is a careful one.
Insulin transports the glucose in our blood (from the food we eat) to our muscles if the "glycogen stores" in the muscle cells need replenishing. The stores of energy need to be replenished most commonly in the morning before we eat breakfast (because we've been fasting all night and used them up in our sleep), and after we exercise (because, again, we've used them up).
So, if you eat carbohydrates following a workout or first thing in the morning, the first place the insulin is going to take those carbs is to your muscle stores.
THIS IS GOOD! ...because if those stores are empty and your body is trying to refill them without extra carbs/insulin, the muscle will continue to break itself down and hinder its ability to build itself stronger.
Powerlifters and bodybuilders who are NOT diabetic, eat large amounts of carbohydrates after a workout because it causes their pancreas to naturally produce more insulin and carry those carbs to the glycogen stores. This is an important part of muscle recovery for an athlete, as Anna explained well in her article last fall. Some people actually get insulin prescriptions from their doctors and attempt to take extra insulin even though their pancreas is making plenty. This is obviously dangerous and plenty of bodybuilders have induced severe hypoglycemic episodes when they aren't careful with their dosing.
When does insulin store carbs as fat? When your glycogen stores don't need to be filled. That's a large reason why low-carb diets help a person reduce bodyfat, because you're eating proteins and fats, which need only a modicum of insulin to be absorbed into the body for fuel. Without the carbs, you use less insulin, without as much insulin, you store less food as fat.
I had great success with a low-carb, higher-protein diet when I first started weightlifting. I followed this plan for a year and lost about ten or twelve pounds while actually putting on about ten pounds of muscle.
As a powerlifter, I had to increase my carbohydrate intake because my muscles are working much differently and being asked to grow stronger much more quickly. My body goes through a lot of calories every day as a result of powerlifting training, therefore I can and need to eat more carbs. Again, though, I don't go carb-crazy. I still focus my carbs at breakfast and after a workout, and at two other meals that day. On the days I don't workout, I eat very low-carb. (And they're usually in the form of plain oatmeal, oat bran, sweet potatoes or CornBran cereal.)