If you look around the forum and read up on anything regarding cables, you'd know that cable makes a difference in how well the audio signals are being passed through. I didn't used to believe that cable made so much difference, until I've heard them myself. Cables do change the characteristic of the sound, sometimes in a dramatic fashion, sometimes very subtle.
Still, the plain fact is they do. So the more cables you have in between your headphone and your source, the more likely the signal will degrade at a certain point, or create some other type of differences.
Of course, if your headphone isn't high-end enough, you probably can't hear the difference. For me, a Shure E5c was definitely able to pick up the difference between using the iPod remote and without. I didn't try the Shure E3c in similar fashions.. perhaps I'll dig them back out and compare them.
Regardless, the wiring quality in the iPod remote isn't all that great.