I have never seen anyone teach balisong as a system on its own. I have always viewed it as another tool that fits into the knife portion of ______(fill in the blank) FMA. Typically the motions learned from a knife system translates to the balisong as well with the addition of a few special techniques as mentioned (pinching, flailing, loaded fist, and manipulation). I thinks its pretty much like a swiss army knife in the states, every boyscout has one, but how much are they formally trained to use the fork on the knife, they already know from a regular fork. The different manipulations probably come playing around with it. When my lolo grandpa gave me my first one he said all the kids have them in the Philippines. Similar to all the yoyo manipulations, it comes from play.
I could be wrong however. There could be a dedicated art on manipulation similar to the Japanese art of drawing the sword, but I've never seen it.