How can pure oil (no gas) get into the sound dampener (breather) without passing through the carb(s)?
It can't by itself. The carbs get a fuel oil mix from the fuel pump. The ouput of the fuel pump to the carbs is fuel + oil already mixed. Now what can happen is if the carbs are flooding like I mentioned before, what happens is the fuel/oil mix pools up wherever its going to pool up. And what happens is the fuel evaporates, but the oil does not, the oil stays behind. So it can "look like" it's pure oil, but it's really not. It's stil a fuel/oil mix, its just that the majority of fuel has evaporated.
Click this picture and print it out, and give it a read. This is the oil system. As you can see, there is only 1 output from the oil pump, and that goes directly to the fuel line on the input side of the fuel pump, where it mixes with fuel
Does the oil system make better sense to you with the picture?