My Gibsons and in fact my strat to some extent do the same thing. I completely re wired with new pots n caps my Gibsons and thought i had messed it up, but they where the same before. I think its the ground in my house tbh.
Quick test, plug the ipod to the amp guitar Jack, low volume, and if its the ground you should hear that hum/buzz as well.
I even bought the Hum-X and made Zero diff