I would have to refer you to engineering textbooks to give you an answer about how a balanced circuit cancels even order distortion, but this type of circuit does do this, and leaves the odd harmonic distortion intact. This cancellation of the even order harmonic distortion occurs only within those stages which are balanced, and does not remove any distortion components generated within any preceeding or later stages which are unbalanced.

Technically, a true balanced circuit refers to one which uses a balancing transformer. This type of circuit is not referenced to ground. This circuit is rare today, even in professional equipment, because of the expense of high quality transformers.

What is now common is what is known as differential or electronically balanced, which achieves balancing by purely electronic means.

Both types however cancel even order harmonic distortion within the circuit.

Push pull output stages in power amplifiers also fall into this category, so that one stage will cancel even order harmonic distortion generated within that stage. Bridged power amplifiers are also a "balanced" circuit and would have the same sonic penalty.

Components such as power amps which are designed as balanced (differential) from input all the way through their outputs are the worst of all worlds, as the entire circuit path will only generate odd order distortion, and probably not sound very good as a result.