I don't understand this thing about "balance" when discussing fore-aft position. Are we talking about being able to hold yourself upright, without your hands on the bars, maybe even riding no-hands? I'm 100% sure I could do that on any bike, regardless of the fore-aft position of the saddle.

The thing that would make that hard is if the saddle were TILTED too far forward, thus tilting your weight forward and forcing weight onto your hands. The balance test might be a good tool for getting saddle tilt just right, but I don't see what it has to do with fore-aft position.