You will find that some grommets are bigger than the others. These would be the shared holes.
I'm with Court-Jester on this. All I do is use an awl to push the string aside, then cut the tip of the string at a sharp angle, use the bent nose pliers to get a good grip on the tip and push it through the hole. After the tip appears on the other side, use the pliers to pull it through. It will be extremely difficut to push it through using your fingers, so just use the pliers.
I tried using the pathfinder in an instance before, it was so tight that the PF awl got stuck in the hole and separated from the holder. PF awl was busted. I had to yank out the needle, and used a normal awl to widen the hole slightly and created a path to push the string through. Have not bothered to get a replacement PF awl since then.
By just using the awl alone, I've not damaged the string, and never had complaints about failure or strings snapping.