Well, I've been playing around - but I haven't got my distortion meter out yet.
I've downloaded Vox
and Quod Libet
audio players. I've opted for the latter because I much prefer the interface.
I get distortion (and I can reproduce this at exact points in the music) on iTunes regardless of how I play the music back - optical cable to DAC, USB cable to DAC or streaming via Airplay. Playback via USB DAC, which works better than optical, is nastily bright and significantly distorted right from the first chords of Sharon Isbin's Journey to the New World
- which is acoustic guitar. It's very unpleasant and not at all realistic, and it distorts regardless of what the iTunes volume control is set to.
Playing the same tracks via Vox or Quod Libet and the optical connection reduces distortion but there is still a tiny amount on peaks. The sound is a bit wooly.
With Quod Libet on USB DAC the sound is more natural and open, has extended bass and no distortion (except for one moment which I suspect is the actual recording), even when the headphones are cranked up high. It's got a better sense of space and 'being there'.
Then I re-ripped it from the CD to FLAC using XLD
with no compression and it's audibly better still. The TEAC HR Audio app improves things even further.
Interestingly, when all apps are set to maximum playback level, they're all the same volume except for iTunes - which plays back much louder.
Both Quod Libet and Vox can play all the files from your iTunes library so I'd suggest you try them and see if you can hear a difference.
I'm still of this opinion that iTunes is just plain nasty.