If you move one side of a bar ,the other side moves. Brake input is slight AND MAKES A DIFFERENCE. Any brake input is going to have some kind of effect.

ok, now I've just had a *duh* moment....I was picturing the "other" brake line as the fulcrum.....but the center (powerlines) will act as the fulcrum (due to the aforementioned higher tension (DUH)....now I need to grab a sharpie marker, put some marks on my lines, and see what's moving (although I'm pretty sure your mental picture is more accurate than mine)......I hope you're happy.......picturing me being dragged through the snow, trying to pay attention to which lines are moving relative to the pulleys, and which ones aren't :P

but seriously.... assuming the fulcrum is the power lines......on a turbo bar, while the brake side goes from relatively neutral to "horsing on the brake" due to the 2x motion effect of pulling on the pulley, if the non-brake side goes from slack, to more-slack, is there any real effect on the non-brake side?

Pay close attention to the kite. If one side goes positive + ,the other goes negative -,and it has the opposite effect on that side of the kite. that is why it goes into a spin. Think propeller blade! If you don't want that to happen then you need handles.