You're on the right track.
I look at it like this:
A signal to be sent over a balanced line is split into two identical signals. One of these then has its polarity reversed, so that it is a mirror image of the other (balanced). These two signals are then sent over two conductors to a receiver. At the receiver one again has its polarity reversed, and the signals are combined to the original signal again.
If another signal is injected into the line during the transit (RF, 60Hz, etc), it will be in equal amounts in each conductor (theoretically, since they are right next to each other). When one signal has its polarity reversed at the receiver, the interference signal will then be a mirror image of itself, and will sum to zero when combined, thus eliminating it.