A balanced connection does not discriminate against even and odd order distortion presented to it's input, but the balanced driver on the sending end and the differential ampifier at the receiving end as a loop will themselves only generate odd order distortion. This has nothing to do with anything outside of the sending and receiving loop. Any distortion of any kind that is present at the input of a balanced driver or a fully balanced amplifier will be passed through unaltered since it doesn't know what is distoriton in the signal and what is the music.

Fully balanced designs (as opposed to balanced connections) were originally developed as a way to reduce distortion. This they do! However they do it by cancelling the amplifier's own even order distortion components and leaving the odd ones intact.

This is exactly like somebody saying that they have "lowered their cholesterol" by eliminating the "good" cholestrol and leaving the "bad" cholesterol!

If you do a Google search under wording like "even order distortion in balanced amplifiers" you will get several references. Many that I got were concerned with push pull stages in tube amplifiers, but you should be able to piece together a picture of when and how this process takes place.

There are designers of course who have differing ideas about the best way to design an amplifier. What I am presenting are some objective facts about the behavior of these types of designs, and their sound quality which has been confirmed in listening tests by myself and those who I've known over the years.

The readers here can do the research if they wish, and draw their own conclusions. I've said about as much as I can about the subject without endlessly repeating myself.