Third wire does not collect interference in a balanced line. Instead, voltage signalling balanced line uses one ground and two signal lines of opposite polarity and input is difference between these two signal lines. Induced interference is more or less the same on both signal lines, therefore cancels out. At a quick glance this article [1] seems to explain this without delving into electronics. Some differential lines (e.g. RS-485, popular in industrial automation) use current signalling thus requiring two wires per signal.
[0]: http://www.cliffuk.co.uk/products/combijacks/combijacks.jpg [1]: http://www.aviom.com/blog/balanced-vs-unbalanced/